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Dissociation  as  Measured  by  the  Freezing 
Point  Lowering  and  by  Conductiv- 
ity— Bearing  on  the  Hydrate  Theory . 
The  Composition    of  the    Hy- 
drates Formed  by  a   Number 
of  Electrolytes. 


DISSERTATION 


SUBMITTED  TO    THE    BOARD  OF  UNIVERSITY  STUDIES  OF 

THE  JOHNS  HOPKINS  UNIVERSITY  IN  CONFORMITY 

WITH  THE  REQUIREMENTS  FOR  THE  DEGREE 

OF  DOCTOR  OF  PHILOSOPHY 


BY 


JAMES  NEWTON  PEARCE. 
BALTIMORE 


June,  1907 


EASTON,  PA.  : 
ESCHENBACH  PRINTING  COMPANY. 

1907. 


Dissociation  as  Measured  by  the  Freezing 
Point  Lowering  and  by  Conductiv- 
ity— Bearing  on  the  HydrateTheory  * 
The  Composition    of  the    Hy- 
drates Formed  by  a   Number 
of  Electrolytes. 


DISSERTATION 


SUBMITTED  TO    THE    BOARD  OF  UNIVERSITY  STUDIES  OF 

THE  JOHNS  HOPKINS  UNIVERSITY  IN  CONFORMITY 

WITH  THE  REQUIREMENTS  FOR  THE  DEGREE 

OF  DOCTOR  OF  PHILOSOPHY 


BY 


JAMES  NEWTON  PEARCE. 

BALTIMORE 

June,  1907 

••    OF  THE 

(  UNIVERSITY  I 


OF 


EASTON,  PA.  : 

ESCHENBACH  PRINTING  COMPANY. 
1907. 


CONTENTS. 

Acknowledgment 4 

Historical 5 

Five  Lines  of  Evidence  for  the  Existence  of  Hydrates  in  Aqueous 

Solutions 6 

Conductivity 18 

Object  of  this  Investigation 21 

Experimental 21 

Conductivity 23 

Specific  Gravity 23 

Volumetric  Apparatus 24 

Solutions 24 

Water 24 

Calculations  for  the  Composition  of  Hydrates 24 

Calcium  Chloride 26 

Strontium  Chloride 30 

Magnesium  Chloride 32 

Barium  Chloride 34 

Calcium  Nitrate 36 

Strontium  Nitrate 38 

Magnesium  Nitrate 40 

Barium  Nitrate 41 

Barium  Bromide 43 

Barium  Iodide 44 

Cobalt  Chloride 44 

Cobalt  Nitrate 47 

Copper  Chloride 50 

Copper  Nitrate 52 

Nickel  Nitrate 53 

Aluminium  Chloride 58 

Sodium  Bromide 60 

.  Hydrochloric  Acid 63 

Nitric  Acid 65 

Sulphuric  Acid 66 

Discussion 68 

Summary 75 

Biography 78 


186986 


ACKNOWLEDGMENT. 

The  author  wishes  to  take  this  opportunity  to  express  his 
gratitude  to   President   Remsen,   Professor   Morse,    Professor 
Jones,  Dr.  Acree,  Dr.  Tingle  and  Dr.  Frazer  for  the  valuable 
instruction  and  advice  received  in  both  lecture  room  and 
laboratory. 

Special  thanks  are  due  Professor  Jones,  at  whose  sugges- 
tion and  under  whose  guidance  this  investigation  was  car- 
ried out. 

The  author  would  also  express  his  appreciation  of  the  in- 
struction received  from  Professor  Ames  and  Professor  Bliss 
in  the  Department  of  Physics. 


V     OF  THE 

UNIVERSITY 

OF 


Dissociation  as  Measured   by  the   Freezing 

Point  Lowering  and  by  Conductivity — 

Bearing  on  the  Hydrate  Theory*  The 

Composition   of  the    Hydrates 

Formed  by  a  Number  of 

Electrolytes* 

HISTORICAL. 

The  work  of  Arrhenius,1  Raoult,2  Loomis,3  Barnes,4  and 
of  Jones  and  his  co-workers5  upon  the  lowering  of  the  freez- 
ing point  of  concentrated  aqueous  solutions  of  electrolytes 
show  clearly  that,  starting  with  the  most  dilute  solutions, 
the  molecular  lowering  decreases,  passes  through  a  minimum 
and  then  increases  with  increasing  concentration. 

Conductivity  measurements  made  by  Jones  and  Knight,8 
and  Jones  and  Chambers,7  over  the  range  of  concentrations 
used  in  the  above  freezing  point  work  showed  no  evidence 
of  a  minimum  when  the  data  were  plotted  in  curves.  Again, 
if  we  assume  the  dissociation  as  measured  by  the  conductiv- 
ity method  to  be  correct  as  represented  by  a  =  — ,  and  from 

/*» 

it  calculate  the  theoretical  molecular  lowerings  in  each  case, 
we  find  that  these  molecular  lowerings  decrease  regularly, 
and,  when  plotted,  show  no  evidence  of  a  minimum. 

It  was  from  the  work  of  Jones  and  Chambers  that  the  first 
tentative  suggestion  was  offered  as  to  the  cause  of  this  phe- 
nomenon. Using  their  own  words,  it  is  this:  "  In  concentra- 
ted solutions  the  salts  must  take  up  a  part  of  the  water,  form- 
ing complex  compounds  with  it,  and  thus  removing  it  from 

1  Ztschr.  phys.  Chem.,  2,  496. 

2  Ibid.,  2,  488. 

3  Wied.  Ann.,  60,  253  (1897);  Ibid.,  57,  503. 

4  Trans.  Roy.  Soc.  of  Canada,  Vol.  VI.,  Sec.  III.,  37. 

5  Ztschr.  phys.  Chem.,  12,  642.     Am.  Chem.  Jour.,  22,  5  (1899).     Ibid.,  22,  110 
(1899).     Ibid.,  23,  89  (1900).     Ibid.,  23,  512  (1900).     Ibid.,  27,  433  (1902).     Ztschr. 
phys.   Chem.,  46,  244.     Ibid.,  49,  385    (1904).     Am.  Chem.  Journ.,  31,  303    (1904). 

.Ibid.,  32,  308  (1904).  Ibid.,  33,  534  (1904).  Memoir  Carnegie  Inst.,  Washington, 
No.  60. 

e  Am.  Chem.  Jour.,  22,  110  (1899). 
7 /&«*.,  23,  89  (1900). 


the  field  of  action  as  far  as  the  freezing  point  lowering  is  con- 
cerned. This  molecular  complex,  which  is  probably  very 
unstable,  acts  as  one  molecule  in  lowering  the  freezing  point 
of  the  remaining  solvent.  Thus  the  total  amount  of  water 
present  acting  as  solvent  is  equal  to  the  total  amount  of  water 
present  diminished  by  that  combined  with  the  salt-molecules. 
By  assuming  that  a  molecule  of  the  salt  is  in  combination 
with  a  large  number  of  molecules  of  water,  it  is  possible  to  ex- 
plain all  of  the  freezing  point  results  obtained. 

"The  conductivity  results  must,  however,  be  taken  into  ac- 
count. These  show,  unmistakably,  a  marked  degree  of  dis- 
sociation even  in  the  most  concentrated  solutions  employed. 
There  must  be,  therefore,  a  certain  number  of  molecules 
broken  down  into  ions,  either  by  the  water  acting  as  a  solvent 
or  by  the  water  in  combination  with  the  salt,  just  as  salts  are 
probably  dissociated  in  their  water  of  crystallization." 

They  also  showed  that  in  the  concentrated  solutions  the 
molecular  lowering  is  often  much  greater  than  the  theoret- 
ical lowering,  if  all  of  the  molecules  were  completely  dissocia- 
ted into  ions.  It  is  only  on  the  assumption  set  forth  by  Jones 
and  Chambers  that  this  phenomenon  can  be  explained. 

Thinking  that  the  hygroscopic  property  of  certain  sub- 
stances might  throw  some  light  upon  the  point  in  question, 
Chambers  and  Frazer,1  at  the  suggestion  of  Jones,  took  up  the 
study  of  the  freezing  point  lowerings  produced  by  copper 
sulphate,  phosphoric  acid,  hydrochloric  acid,  sodium  acetate, 
cadmium  iodide,  zinc  chloride,  and  strontium  iodide,  com- 
pounds with  very  great  affinity  for  water.  In  all  cases  well 
defined  minima  were  obtained,  and  from  these  minima  the 
freezing  point  lowerings  increased  with  increasing  concen- 
tration, this  substantiating  the  view  put  forth  by  Jones  and 
Chambers. 
Evidence  for  the  Existence  of  Hydrates  in  Aqueous  Solutions 

i.  Relation  between  the  Water  of  Crystallization  and  the 
Temperature  at  which  the  Salts  Crystallize. — If  the  assump- 
tion is  true,  that  we  are  actually  dealing  with  hydrates,  un- 

1  Am.  Chem.  Jour.,  23,  512  (1900). 


stable  complex  molecules  of  solvent  and  dissolved  substance, 
then  we  should  expect  that  the  complexity  of  these  hydrates 
would  vary  with  the  temperature,  and  with  the  existing  con- 
ditions. That  such  is  the  case  is  proved  by  the  fact  that 
almost  all  of  the  water  except  that  which  is  held  as  water 
of  crystallization  may  be  removed  from  solutions  of  salts 
at  the  boiling  point  of  these  solutions.  Furthermore,  the 
same  results  are  obtained  by  spontaneous  evaporation  of 
the  solvent  from  the  solutions  under  reduced  pressure  at 
ordinary  temperatures.  What  is  still  more  striking,  as  we 
shall  see  in  a  subsequent  discussion  in  this  paper,  is  that  these 
same  molecular  complexes  may  be  broken  down  to  some  ex- 
tent even  in  solution  by  the  addition  of  a  strong  "  dehydrating" 
agent.  It  is  not  to  be  assumed,  however,  that  the  resulting 
hydrate  formed  in  the  above  three  cases  is  the  same.  The 
very  large  number  of  cryoscopic  measurements,  which  have 
been  made  in  this  laboratory,  gives  conclusive  evidence  that 
salts  which  crystallize  with  water  of  crystallization  do  com- 
bine with  a  much  larger  quantity  of  water  when  in  solution 
at  ordinary  temperature. 

If,  then,  the  amount  of  water  with  which  a  salt  can  crys- 
tallize from  a  solution  is  a  function  of  the  temperature,  we 
should  expect  this  amount  of  water  to  be  larger,  the  lower 
the  water  at  which  the  crystals  are  formed. 

We  also  have  a  class  of  substances  which,  under  ordinary 
conditions,  crystallize  from  solution  without  water  of  crys- 
tallization, e.  g.,  the  chlorides  of  potassium  and  ammonium, 
and  the  nitrates  of  potassium,  ammonium,  sodium,  and  bar- 
ium. 

This  is  no  doubt  due,  in  some  measure,  to  the  temperature 
at  which  these  substances  have  been  allowed  to  crystallize. 
It  is  well  known  that  conditions  can  be  secured  under  which 
some  of  these  substances  separate  from  solution  with  small 
amounts  of  water  of  crystallization.  It  is  still  more  proba- 
ble, as  we  shall  see  later,  that  even  the  so-called  anhydrous 
salts  have  considerable  hydrating  power  in  dilute  solution. 

2.  Relation    between    the    Water    of    Crystallization    and    the 


8 

Lowering  of  the  Freezing  Point. — An  extensive  investigation 
of  the  freezing  point  lowerings  produced  by  aqueous  solu- 
tions of  electrolytes  carried  out  by  Jones  and  Getman,1  and  by 
Jones  and  Bassett,2  has  established  the  fact  that  there  exists 
between  the  lowering  of  the  freezing  point  arid  the  water  of 
crystallization  this  general  relation;  namely,  that  the  magni- 
tude of  the  freezing  point  lowering  of  a  solution  of  any  given 
electrolyte  is  directly  dependent  upon  the  number  of  mole- 
cules of  water  with  which  that  salt  crystallizes  from  solu- 
tion. 

A  brief  summary  of  this  work,  to  which  reference  must  be 
made  to  the  curves  in  the  original  article,  will  bring  out  more 
clearly  this  relation. 

If  we  consider  the  chlorides  of  the  alkali  group,  all  of  which 
are  binary  salts,  we  find  that  the  anhydrous  salts,  sodium 
chloride,  potassium  chloride,  and  ammonium  chloride,  give 
approximately  the  same  depression  of  the  freezing  point  with 
increasing  concentration.  Lithium  chloride,  with  two  mole- 
cules of  water  of  crystallization,  gives  a  considerably  greater 
depression  for  the  same  concentrations. 

The  ternary  chloride  of  calcium,  strontium,  magnesium, 
each  of  which  crystallizes  with  six  molecules  of  water,  give 
depressions  of  the  same  order  of  magnitude,  yet  considerably 
greater  than  those  of  the  alkali  group.  Barium  chloride, 
with  two  molecules  of  water  of  crystallization,  gives  depres- 
sions lower  than  those  produced  by  the  other  members  of  the 
alkali-earth  group,  yet  greater  than  those  produced  by  lith- 
ium with  the  same  number  of  molecules  of  water  of  crystalli- 
zation. 

This  is  to  be  accounted  for  by  the  fact  that  lithium  chlor- 
ide is  a  binary  electrolyte,  yielding  two  ions  while  baruim 
chloride  is  a  ternary  electrolyte  yielding  three  ions.  Again 
we  find  that  the  chlorides  of  iron,  aluminium,  and  chromium, 
which  separate  from  solution  with  six  molecules  of  water, 
give  much  greater  depressions  of  the  freezing  point  than  do 

1  Memoir   Carnegie   Inst. ,  Washington ,   No.    60.     Ztschr|  phys.    Chem.,  46,    244 
(1903);  49,  385   (1904). 

2  Am.  Chem.,  Jour.,  33,  534  (1905);  34,  290  (1905). 


the  chlorides  of  magnesium,  calcium,  and  strontium.  This 
is  just  what  we  should  expect  when  we  consider  that  the  mem- 
bers of  the  iron  group  form  quarternary  salts  while  those  of 
the  alkali-earth  group  form  ternary  salts. 

Similar  relations  are  found  to  exist  between  the  bromides, 
iodides,  and  nitrates  of  these  metals. 

If,  however,  we  compare  the  molecular  depressions  produced 
the  bromides  and  iodides  of  potassium,  sodium  and  lithium, 
we  find  that  in  each  case  the  sodium  salts  with  two  molecules 
of  water  give  greater  depressions  than  do  the  potassium  salts 
crystallizing  without  water,  yet  smaller  depressions  than  do 
the  corresponding  lithium  salts  crystallizing  with  three  mole- 
cules of  water. 

Barium  bromide,  with  two  molecules  of  water  of  crystalli- 
zation, shows  a  greater  depression  than  does  lithium  bromide 
with  three  molecules,  just  as  we  should  expect;  it  also  gives  a 
smaller  lowering  than  do  the  bromides  of  calcium,  strontium, 
and  magnesium,  each  of  which  has  six  molecules  of  water  of 
crystallization. 

The  nitrates  of  sodium,  potassium,  and  ammonium,  which 
crystallize  without  water,  give  the  smallest  lowerings  of  the 
freezing  point,  while  lithium  nitrate,  with  two  molecules, 
comes  next  in  the  order  of  magnitude.  About  midway  be- 
tween lithium  nitrate  and  those  salts  which  crystallize  with 
six  molecules  of  water,  lie  the  values  for  calcium  nitrate,  which 
has  but  four  molecules  of  water. 

The  nitrates  of  aluminium,  chromium,  and  iron  crystal- 
lizing with  eight  and  nine  molecules,  respectively,  give  the 
greatest  lowerings  of  any  salts  so  far  studied.  Comparing 
the  chlorides,  bromides,  iodides,  and  nitrates  of  the  alkali 
group  which  crystallize  without  water,  we  find  that  they  all 
show  a  molecular  lowering  of  the  same  order  of  magnitude 
for  the  dilute  solutions,  and  this  increases  very  slightly,  if 
at  all. 

Lithium  chloride  and  lithium  nitrate,  each  crystallizing  with 
two  molecules,  give  approximately  the  same  molecular  lower- 
ings. The  same  relation  holds  for  lithium  bromide  and  lith- 


IO 

him  iodide,  which  crystallizes  with  three  molecules.  Further, 
the  molecular  lowerings  produced  by  the  nitrate  and  chloride 
are  less  than  those  produced  by  the  bromide  and  iodide  of 
lithium. 

Owing  to  the  slight  solubility  of  barium  chloride,  com- 
parisons between  it  and  the  bromide  andiodide  can  be  made 
only  in  dilute  solutions.  At  these  concentrations  all  three 
salts  give  molecular  lowerings  of  approximately  the  same 
order  of  magnitude.  In  the  more  concentrated  solutions 
the  iodide  gives  a  greater  lowering  than  the  bromide. 

The  chlorides,  bromides,  and  iodides  of  the  alkali-earths, 
which  crystallize  with  six  molecules  of  water,  give  lowerings 
of  the  freezing  point  which  are  of  approximately  the  same 
order  of  magnitude.  As  in  the  case  of  the  alkali  metals,  the 
bromides  give  somewhat  greater  lowerings  than  the  chlor- 
ides, and  the  iodides  still  greater  lowerings  than  the  bromides. 

The  nitrates  produce  about  the  same  lowerings  as  the  cor- 
responding chlorides  which  crystallize  with  the  same  number 
of  molecules  of  water,  and,  therefore,  somewhat  less  than 
the  corresponding  bromides  and  iodides. 

In  other  words,  if  we  consider  in  any  one  group  those  salts 
which  separate  from  solution  with  the  same  number  of  mole- 
cules of  water,  we  find  that  they  produce  molecular  lowerings 
of  approximately  the  same  order  of  magnitude.  If,  on  the 
other  hand,  the  salts  in  the  same  group  combine  with  vary- 
ing amounts  of  water  of  crystallization,  those  salts  having 
the  greater  combining  power  will  produce  the  greater  molecu- 
lar lowerings,  and  -vice  versa. 

Again,  since  the  hydrating  power  is  a  function  of  the  water 
of  crystallization,  the  greater  .the  number  of  molecules  of 
water  with  which  a  salt  crystallizes  from  solution,  the  greater 
will  be  the  amount  of  water  removed  from  the  field  of  action 
as  solvent,  and,  hence,  the  greater  will  be  the  abnormality  in 
the  freezing  point  lowering,  due  to  this  increase  in  concentra- 
tion. 

These  facts  give  conclusive  evidence  of  the  truth  of  the 
theory  advanced  by  Jones  and  Chambers1  to  account  for  the 

1  Am.  Chem.  Jour.,  23,  89  (1900). 


II 

great  abnormalities  "that  in  solution  the  dissolved  substance 
is  combined  with  a  part  of  the  solvent,  the  amount  of  the 
solvent  held  in  combination  by  the  dissolved  substance  being 
a  function  of  the  concentration  of  the  solution." 

j.  Relation  between  the  Minima  in  the  Molecular  Lower- 
ing of  the  Freezing  Point  and  the  Molecular  Elevation  of  the 
Boiling  Point. — A  short  series  of  boiling  point  measurements 
was  carried  out  in  this  laboratory  by  Jones  and  Getman.1 
They  worked  with  aqueous  solutions  of  potassium,  sodium, 
lithium  and  barium  chloride,  potassium  and  sodium  carbon- 
ates, and  sodium  sulphate. 

In  all  cases  slight  but  well-defined  minima  were  obtained. 
These  occur  at  somewhat  greater  concentrations  than  do  the 
minima  in  the  freezing  point  lowerings  for  the  same  electro- 
lytes. That  this  is  so  is  not  surprising,  since  I  have  already 
pointed  out  that  the  complexity  of  the  hydrates  is  decreased 
by  increase  in  temperature.  Hence,  the  amount  of  water  re- 
moved from  the  field  of  solvent  is  less  than  at  the  freezing 
temperature.  Therefore,  a  greater  concentration  is  required 
in  order  that  the  effect  due  to  hydration  may  counterbalance 
the  effect  due  to  decrease  in  dissociation. 

4.  The  Bearing  of  Hydrates  on  the  Temperature  Coefficient 
of  Conductivity  of  Aqueous  Solutions. — The  conductivity  of 
a  solution  is,  according  to  Ostwald,  represented  thus:  fiv  = 
a(c  +  a)  when  c  and  a  represent  the  velocities  of  the  cation 
and  anion  respectively,  and  a.  the  dissociation  at  the  given 
volume.  Increase  in  conductivity  may  be  brought  about  in 
two  ways,  either  by  increase  in  dissociation  or  by  increasing 
the  velocities  of  the  ions. 

It  is  a  well-known  fact  that  increase  of  temperature  greatly 
increases  the  conductivity.  Is  this  due  to  an  increase  in  the 
velocity  of  the  ions,  or  to  an  increase  in  dissociation?  In  an 
extended  study  of  the  temperature  coefficients  of  conduc 
tivity  in  aqueous  solutions,  and  on  the  effect  of  temperature 
on  dissociation,  it  was  found  by  Jones  and  West2  that  the 

1  Ztschr.  phys.  Chem.,  46,  244  (1903).     Memoir  Carnegie  Inst.,  Washington,  No 
60,  p.  12. 

1  Am.  Chem.  Jour.,  34,  357  (1905) 


12 

dissociation  of  electrolytes  decreases  slightly  with  rise  in 
temperature  between  o°  and  35°.  Noyes  and  Coolidge,1 
working  at  high  temperature,  have  found  that  the  dissocia- 
tion decreases  rapidly  with  rise  in  temperature.  This  is  just 
what  we  should  expect  from  our  knowledge  of  the  fact  that 
the  dissociating  power  of  the  solvent  is  a  function  of  its  own 
association.  Since  the  association  of  the  solvent  decreases 
with  increase  in  temperature,  so  should  the  dissociation  of 
the  electrolyte  decrease,  as  has  been  found  to  be  the  case. 

Since,  then,  we  cannot  attribute  the  increase  in  conduc- 
tivity with  rise  in  temperature  to  an  increase  in  the  dissocia- 
tion of  the  electrolyte,  we  must  conclude  that  the  increase 
in  conductivity  with  rise  in  temperature  is  due  to  an  increase 
in  the  velocity  of  the  ions. 

The  velocity  of  the  ions  depends  first  upon  the  driving  power 
or  kinetic  energy,  (2)  upon  the  mass  of  the  ion,  and  (3)  upon 
the  viscosity  of  the  medium.  It  is  a  well-known  fact  that 
ions  of  small  atomic  masses  move  much  more  rapidly  than 
those  of  higher  atomic  mass.  Also,  that  increase  in  tempera- 
ture of  a  given  medium  increases  the  kinetic  energy  of  all 
particles  in  that  medium.  Increase  in  temperature  also  de- 
creases the  viscosity  of  the  medium,  thereby  decreasing  the 
"internal  friction"  of  the  ions. 

All  of  these  factors  would  increase  the  velocity  with  which 
the  ions  move,  and,  consequently,  increase  the  conductivity 
as  the  temperature  is  raised. 

Jones2  has  advanced  another  idea  to  account  for  the  in- 
crease in  conductivity  with  increase  in  temperature.  "The 
mass  of  the  ion  decreases  with  rise  in  temperature.  This 
does  not  refer  to  the  charged  atom  or  group  of  atoms  which 
we  usually  term  the  ion,  but  to  this  charged  nucleus  plus  a 
larger  or  smaller  number  of  molecules  which  are  attached  to 
it,  and  which  the  ion  must  drag  along  with  it  through  the 
remainder  of  the  solvent. 

"That  the  ions  are  hydrated  seems  to  have  been  shown  al- 
most beyond  question  by  Jones  and  his  co-workers.  That 
these  hydrates  are  relatively  unstable  has  also  been  demon- 

1  Ztschr.  phys.  Chem.,  46,  323  (1903). 

2  Memoir,  Carnegie  Inst.,  Washington,  No.  60,  p.  157. 


13 

strated;  therefore,  the  higher  the  temperature,  the  less  com- 
plex the  hydrate  existing  in  solution.  The  less  the  number 
of  molecules  of  the  solvent  combined  with  the  ion,  the  smaller 
the  mass  of  the  ion,  and  the  less  its  resistance  when  moving 
through  the  solvent;  consequently,  the  ion  will  move  faster 
at  the  higher  temperature. 

"If  this  factor  of  diminishing  complexity  of  the  hydrate  formed 
by  the  ion  with  rise  in  temperature,  plays  a  prominent  r61e 
in  determining  the  large  temperature  coefficient  of  conduc- 
tivity, then  we  should  expect  to  find  those  ions  with  the  largest 
hydrating  power  having  the  largest  temperature  coefficients 
of  conductivity.  The  more  complex  the  hydrate,  i.  e.,  the 
greater  the  number  of  molecules  of  water  combined  with  an 
ion,  the  greater  the  change  in  the  complexity  of  the  hydrate 
with  rise  in  temperature." 

Reference  to  the  experimental  data  obtained  by  Jones 
and  West1  shows  how  well  this  idea  is  substantiated  by  the 
facts.  To  show  this  we  give  the  following  table.  In  the 
first  column  are  given  those  salts  which  crystallize  from  solu- 
tion with  no  water  of  crystallization  and  which,  therefore, 
have  but  slight  hydrating  power  in  solution.  In  the  second 
column  are  placed  those  salts  which  crystallize  with  large 
amounts  of  water,  and  which,  consequently,  have  great  hydra- 
ting  power. 

Substances  with  slight  hydrating  power.        Substances  with  large  hydrating  power. 
Temp,  coefficients  in  Temp,  coefficients  in 

conductivity  units.  conductivity  units. 

Z/  =  2.  V=  1024. 

NH4C1  2.07  2.94 

NH4Br  2.16  2.86 

KC1  2.13  2.84 

KBr  2.18  2.91 

KI  2.09  2.91 

KNO3  1.86  2.71 


Z>=  2. 

v  =  1024. 

CaCl2 

3-n 

5.61 

CaBr2 

3.01 

5-20 

SrBr2 

2-93 

5.27 

BaCl2 

2.86 

5.30 

MgCl2 

2-55 

4-59 

MnCl2 

2-37 

4.86 

Mn(N03)2 

2.24 

4.  16 

CoCl2 

2-54 

4-95 

Co(N03)2 

2.48 

4.67 

NiCl2 

2.63 

5-04 

Ni(N03)2 

2-51 

4.58 

CuCl2 

2.15 

5-04 

Cu(N03)2 

2.38 

4.88 

i  Am.  Chem.  Jour.,  34,  357  (1905). 


14 

From  the  points  brought  out  in  (i)  we  can  assume,  approxi- 
mately, that  the  hydrating  power  of  salts  in  solution  is  propor- 
tional to  their  water  of  crystallization.  If  this  assumption  is 
correct,  we  should  expect  to  find  that  salts,  having  the  same 
amounts  of  water  of  crystallization,  i.  e.,  the  same  hydrating 
power,  will  have  the  same  temperature  coefficients  of  con- 
ductivity, and  such  we  find  to  be  the  case.  Further,  the  values 
of  the  temperature  coefficients  for  a  given  concentration  in  either 
column  are  the  same  order  of  magnitude,  those  in  the  second 
column,  in  each  case,  being  higher  than  the  corresponding 
values  in  the  first  column,  as  we  should  expect  from  the  greater 
hydrating  power  of  the  former.  It  will  be  seen  that  the  tem- 
perature coefficients  for  v  =  1024  are  higher  in  every  case 
than  for  v  =  2,  for  each  individual  salt.  The  greater  the  dilu- 
tion, the  greater  the  complexity  of  the  hydrate  formed  and 
the  greater  will  be  the  change  in  the  composition  of  the  hydrate 
with  change  of  temperature.  Consequently,  the  tempera- 
ture coefficient  of  conductivity  is  greater  the  more  dilute  the 
solution.  Again,  the  differences  in  value  between  the  tem- 
perature coefficients  for  v  =  2  and  v  =  1024  is  very  much 
smaller  in  case  of  salts  belonging  to  the  first  column  than  the 
corresponding  differences  for  the  salts  of  the  second.  In  other 
words,  the  temperature  coefficients  of  conductivity  increase 
more  rapidly  with  dilution  for  salts  of  greater  hydrating  power. 

5.  The  Absorption  Spectra  of  Certain  Colored  Salts  in  Aqueous 
Solution  as  Affected  by  the  Presence  of  Certain  Other  Salts  with 
Large  Hydrating  Power. — It  has  long  been  known  that  aqueous 
solutions  of  copper  and  cobalt  halide  salts,  when  treated  with 
hydrochloric  acid  gas,  calcium  chloride,  zinc  chloride,  alu- 
minium chloride,  and  other  strong  dehydrating  agents,  un- 
dergo a  change  in  color.  Thus,  when  an  aqueous  solution 
of  cobalt  chloride  is  treated  with  a  little  solid  calcium  chlor- 
ide or  a  concentrated  solution  of  this  salt,  the  initial  purple- 
red  color  is  changed  to  blue.  Likewise,  the  green  concentra- 
ted solution  of  cupric  chloride,  when  diluted,  becomes  blue, 
and  when  the  resulting  solution  is  evaporated  or  treated 
with  a  dehydrating  agent  the  original  green  color  returns. 


15 

This  change  in  color  takes  place  regardless  of  the  kind  of  sub- 
stance used  as  a  dehydrating  agent.  One  particularly  striking 
fact  is  this:  the  quantities  of  the  dehydrating  agents  required 
to  produce  the  same  change  in  color  are  almost  universely 
proportional  to  the  number  of  molecules  of  water  with  which 
each  salt  crystallizes  from  solution. 

A  similar  color  change  is  met  with  if  we  heat  to  a  high  tem- 
perature solutions  of  colored  electrolytes  in  sealed  tubes. 
This  phenomenon  falls  directly  in  line  with  the  theory  which 
has  been  advocated  by  Jones,  that  for  each  concentration  of 
a  solution  of  an  electrolyte  we  have  a  definite  molecular  com- 
plex for  a  definite  temperature,  which  breaks  down  with  in- 
creasing temperature. 

Many  views  have  been  put  forth  to  explain  these  color  changes. 
Jones  and  Uhler1  undertook  a  spectrographic  study  of  the  ab- 
sorption spectra  of  solutions  of  colored  electrolytes. 

The  phenomenon  of  absorption  is  one  of  resonance.  The 
waves  have  definite  periods  and  definite  amplitudes.  If, 
now,  these  waves  meet  some  medium  containing  particles 
which  vibrate  with  the  same  or  nearly  equal  periods,  the  energy 
of  the  wave  is  given  up  in  setting  the  particle  into  vibration 
and  the  light  is  absorbed,  as  we  say.  We  have  the  natural 
law  that  "that  energy  of  vibration  of  a  given  period  will  be 
absorbed  to  the  greatest  extent  by  a  system  whose  natural 
period  of  vibration  is  most  nearly  equal  to  its  own."  If  the 
period  of  the  vibration  of  the  light  wave  differs  appreciably 
from  that  of  the  system  of  particles,  we  shall  have  much  less 
absorption. 

If  the  mass  of  the  vibrating  particles,  the  hydrate,  is  in- 
creased by  the  addition  of  more  water,  while  the  energy  of 
vibration  remains  the  same,  the  period  of  vibration  will  be 
damped,  and  when  tested,  spectroscopically,  the  absorption 
bands  will  be  found  to  grow  smaller  and  smaller  as  the  com- 
plexity of  the  hydrate  increases. 

If,  on  the  other  hand,  we  decrease  the  mass  of  the  hydrate 
while  the  energy  of  vibration  remains  constant,  the  electrons 

1  Am.  Chem.  Jour.,  37,  126    (1907).     Memoir,  Carnegie   Inst.,  Washington,  No- 
60. 


16 

in  the  hydrated  molecule  will  vibrate  in  resonance  with  a  larger 
number  of  ether  waves,  and  the  result  will  be  that  we  will 
have  a  broadening  of  the  absorption  bands. 

They  first  studied  the  absorption  spectra  of  a  series  of  aque- 
ous solutions  of  cobalt  chloride,  copper  chloride,  and  copper 
bromide. 

They  found  that,  with  increase  in  concentration  of  the  cobalt 
salt  alone,  the  absorption  bands  widen  out  rapidly.  This 
is  just  what  we  should  expect  from  the  results  of  the  freezing 
point  work.  It  has  been  found  from  this  work  that  the  hydra- 
tion  per  molecule  decreases  with  increase  in  concentration. 
In  the  dilute  solutions  we  have  the  largest  hydrates.  These 
have  small  amplitudes  and  long  periods,  hence  they  will  re- 
spond to  fewer  light  waves.  The  result  then  should  be  a 
narrowing  of  the  absorption  bands,  and  such  is  found  to  be 
the  case.  On  adding  more  of  the  salt  it  removes  some  of  the 
water  of  the  solution  from  the  field  of  solvent,  thus  render- 
ing the  large  hydrates  which  previously  existed  unstable  un- 
der the  new  conditions.  As  a  result,  the  former  large  hydrates 
break  down  into  simpler  forms,  which  will  vibrate  in  reso- 
nance with  a  larger  number  of  waves.  The  result  is  a  widen- 
ing of  the  absorption  bands. 

Jones  and  Uhler  next  added  strong  hydrating  agents,  such 
as  calcium  chloride  and  aluminium  chloride,  to  other  series 
of  similar  solutions  of  the  same  salts.  On  the  basis  of  our 
theory  the  dehydrating  agent  will  remove  some  of  the  water 
from  the  field  as  solvent,  thereby  producing  the  same  effect 
as  increasing  the  concentration  of  the  colored  salt  alone. 

A  study  of  the  spectrograms  shows  this  to  be  the  fact. 
Also  keeping  the  concentration  of  the  colored  salt  constant, 
as  the  concentration  of  the  dehydrating  agent  is  increased, 
the  absorption  bands  broaden  with  marked  regularity. 

Spectrograms  were  made  of  these  colored  salts  in  solutions 
of  ethyl  and  methyl  alcohol,  and  acetone,  also  in  binary  mix- 
tures of  solvents  in  which  water  was  the  second  solvent. 

From  the  work  of  Jones  and  Getman1  and  Jones  and  Mac- 

1  Am.  Chem.  Jour.,  31,  339  (1904). 


17 

Master1  it  was  shown  that  these  solvents  do  not  possess  any 
very  great  power  to  combine  with  salts  in  solution.  This 
being  the  case,  if  we  should  take  a  solution  of  copper  chloride 
in  ethyl  alcohol,  the  dissolved  substance,  forming  no  com- 
plex with  the  solvent,  would  be  free  to  vibrate  in  resonance 
with  a  large  number  of  wave  lengths,  and  would,  therefore, 
increase  the  width  of  the  absorption  bands.  The  spectro- 
grams show  wider  bands  than  for  aqueous  solutions.  As 
water  was  added  in  varying  quantities  the  absorption  bands 
became  narrower,  showing  the  damping  effect  due  to  increas- 
ing hydration. 

Here,  again,  the  facts  most  beautifully  confirm  the  theory. 

Before  leaving  this  chapter  we  will  sum  up  our  evidence 
for  the  existence  of  hydrates  in  solutions  of  electrolytes. 

1.  In  the  case  of  all  electrolytes  there  exists  between  the 
water  of  crystallization  and  the  temperature   at   which   the 
crystals  are  formed  a  definite  relation  which,  under  the  same 
conditions,  is  constant  for  a  given  salt.     With  increasing  dilu- 
tion the  molecules  and  ions  of  an  electrolyte  are  able  to  take 
up   a  part  of  the  solvent,  forming  unstable  molecular  com- 
plexes or  hydrates. 

For  equivalent  concentrations  the  complexity  of  the  hy- 
drates formed  by  different  salts  stands  in  close  relation  to  the 
amounts  of  water  with  which  those  salts  crystallize  from  solu- 
tion. 

2.  The   abnormality   in  the   freezing  point   lowerings   pro- 
duced by  solutions  of  electrolytes  is  a  function  of  the  water 
of   crystallization    of   these    electrolytes.     Those    salts   which 
have  a  greater  number  of  molecules  of  water  of  crystalliza- 
tion always  produce  the  greater  lowering  of  the  freezing  point. 
The  same  relation  has  been  found  to  hold  for  the  molecular 
rise  of  the  boiling  point. 

3.  The   minima   in   the   boiling  point   and    freezing   point 
curves  occur  at  those  concentrations  at  which  the  effect  of 
hydration  just  balances  that  produced  by  a  decrease  in  the 
dissociation  of  the  electrolyte.     Owing  to  the  instability  of 
the  hydrates  formed  with  rise    in  temperature,  the  minima 

1  Am.  Chem.  J.,  35,  316  (1906). 


i8 

for  the  boiling  point  curves  occur  at  greater  concentrations 
than  those  for  the  freezing  point  curves. 

4.  The    temperature    coefficients    of    conductivity   increase 
with    increasing   dilution.     For   salts   which   crystallize   with 
the  same  amounts  of  water  the  temperature  coefficients  are 
of   the   same   order   of   magnitude.     Comparing   salts   which 
crystallize   with   different   amounts  of   water,   that   one   will 
have  the  largest  temperature  coefficient  of  conductivity  which 
has  the   greatest   power   to   combine  with   the    solvent.     In 
other  words,  the  greater  the  power  to  bring  water  out  of  solu- 
tion, as  water  of  crystallization,  the  more  complex  will  be 
the   hydrate  formed.     The   more   complex  the   hydrate,   the 
greater  will  be  the  temperature  coefficient  of  conductivity. 

5.  The   absorption  bands  produced   by   aqueous   solutions 
of  colored  electrolytes  widen  with  increase  in  concentration. 
The  same  effect  is  produced  when  an  indifferent  substance 
of  strong  dehydrating  power  is  added.     Similarly,  increasing 
dilution,  with  its  accompanying  increasing  hydration,  decreases 
the  width  of  the  absorption  bands. 

Conductivity. 

The  conductivity  of  a  solution  of  an  electrolyte  is  a  func- 
tion of  several  conditions:  the  nature  of  the  electrolyte 
and  the  degree  of  its  dissociation;  the  speed  of  its  component 
ions;  and  the  viscosity  of  the  solvent.  The  degree  of  disso- 
ciation, in  turn,  depends  upon  the  concentration  of  the  elec- 
trolyte and  the  nature  of  the  solvent. 

As  was  pointed  out  by  Dutoit  and  Aston,  that"  solvent 
whose  molecules  are  associated  to  the  greatest  extent  has 
the  greatest  dissociating  power. 

Weak  acids,  weak  bases,  and  salts  of  weak  acids  and  bases 
show  constantly  increasing  dissociation  with  increasing  dilu- 
tion, but,  within  the  limits  of  accuracy  of  our  present  methods, 
no  maximum  of  conductivity  is  directly  obtainable.  On 
the  other  hand,  strong  electrolytes  show  rapidly  increasing 
dissociation  with  slight  increase  in  dilution — a  maximum  con- 
ductivity being  reached  at  moderate  dilution. 

It  is  stated  by  Ostwald1  that  the  anions  of  the  halogen  acids 

»  Lehrbuch,  2.  679. 


19 
move  more  rapidly  than  do  those  of  the  oxyhalogen  acids, 

e.  g.,  C1O3,  BrO3,  IO3;  that  C1O4  has  a  greater  migration  veloc- 
ity than  IO4.  In  general,  the  more  complex  the  ion,  the  slower 
its  migration  velocity.  Especially  is  this  the  case  with  the 
anions  of  organic  acids.  With  isomeric  anions,  however, 
the  velocities  are  approximately  equal.  With  increasing 
increments  of  CH2  the  velocity  decreases  regularly.  The  same 
may  be  said  with  regard  to  the  organic  cations. 

It  has  been  proved  by  Jones  and  Getman  and  by  Loomis1 
that  organic  acids  are  not  hydrated.  It  is  clear  that  increase 
in  ionic  volume  is  accompanied  by  decrease  in  ionic  speed, 
doubtless  due  to  increase  in  friction  between  ion  and  solvent. 

With  this  idea  in  mind,  and  with  the  evidence  from  the 
freezing  point  measurements  that  the  ions  form  more  and 
more  complex  hydrates  with  increasing  dilution,  we  are  forced 
to  believe  that  the  conductivities  of  solutions  of  strong  elec- 
trolytes are  less  than  they  would  be,  theoretically,  if  there 
were  no  hydration,  by  an  amount  which  is  a  function  of  the 
volume  of  the  ionic  complex. 

Vollmer2  determined  the  values  of  A^  for  solutions  of  potas- 
sium acetate,  sodium  acetate,  potassium  iodide,  lithium 
iodide,  lithium  chloride,  and  silver  nitrate,  in  water  and  alco- 

hol.    He  found  the  relation  —^  -  -  —  =   K   =   0.33  to   hold 


in  every  case. 

Kawalki3  found  the  same  relation  to  exist  between  the 
speeds  of  diffusion  of  the  same  electrolytes  in  water  and  alco- 
hol. It  is  of  especial  interest  to  note  that  the  value  which 

he  obtained  for  his  constant  •=:—        -  =  K'  =  0.33  is  the  same 

D  water 

as    that    found    by    Vollmer    for    conductivity.     From    their 
results  we  obtain  the  relation, 

A/  oo  :  *oo   ::  D'  :  D. 
That  this  relation  will  hold,  in  case  there  is  hydration  or  alco- 

1  Wied.  Ann.,  60,  523  (1897). 

2  Ibid.,  52,  328  (1894). 
8  Ibid.,  52,  300  (1894). 


20 

holation,  is  highly  probable t  since  the  resistance  offered  to 
the  ionic  complex  will  be  the  same  in  each  case. 

As  stated  by  Jahn,1  "recent  measurements  have  made  it 
probable  that  the  mobility  of  the  ions  is  not  independent  of 
their  concentration,  that  they  have  greater  mobility  in  more 
concentrated  than  in  more  dilute  solutions."  Reference  to 
the  work  of  Jones  and  Bassett2  shows  that  this  is  just  what 
we  should  expect.  They  found,  by  freezing  point  measure- 
ments, that  the  hydration  per  gram  molecule  of  the  electro- 
lyte decreases,  with  increasing  concentration,  to  a  certain 
concentration  corresponding  to  the  minimum  in  the  molecular 
lowering  of  the  freezing  point,  and  then  decreases  very  slowly 
with  increasing  concentration.  In  the  more  concentrated 
solutions,  then,  we  have  smaller  changes  in  hydration;  there- 
fore, smaller  changes  in  the  ionic  volumes;  hence,  we  should 
have  smaller  changes  in  the  mobility  of  the  ions. 

That  the  conductivity  depends,  in  no  small  degree,  upon 
the  viscosity  of  the  solution  has  been  known  for  a  long  time, 
yet  the  simultaneous  action  of  the  two  conditions,  dissocia- 
tion and  viscosity,  renders  it  impossible  to  separate  their 
effects.  No  simple  relation  exists  other  than  that  the  conduc- 
tivity decreases  with  increase  in  viscosity. 

G.  Wiedemann3  first  called  attention  to  the  fact  that  the 
friction  which  the  ions  produce  in  their  motion  changes  in  the 
sense  that  the  fluidity  changes.  Accordingly,  the  mobility 
of  the  ions  should  be  a  function  of  the  fluidity  of  the  solution. 

That  the  conductivity  does  not  depend  exclusively  upon 
the  fluidity  can  be  seen  in  the  following  case:  A  i  per  cent 
(by  volume)  solution  of  cane  sugar  and  a  2.2  per  cent  solu- 
tion of  methyl  alcohol  have  the  same  internal  friction,  mz.y 
1.046,  but  the  conductivity  of  potassium  chloride  in  a  i  per 
cent  sugar  solution  is  decreased  3  per  cent,  while  in  2.2  per 
cent  methyl  alcohol  it  is  decreased  3.85  per  cent. 

Pissarjewski  and  Lemcke4  made  the  simple  assumption 
that  the  conductivity  is  directly  proportional  to  the  disso- 

1  Grundriss  der  Electrochemie,  p.  143. 
*  Am.  Chem.  J.,  33,  534  (1905). 
.       «  Pogg.  Ann.,  99,  228  (1856). 

«  Z.  physik.  Chem.,  52,  479  (1905). 


21 

elation,  and  inversely  proportional  to  the  viscosity,  e.  g.,. 
fi  =  K — .  At  maximum  disociation  K  =  Moo  ^oo  •  There- 
fore, the  dissociation  is  a'  =  — v— —  and  not  a 


Moo  ^oo  Moo 

In     thfe    dilutions    which    they     used    the    K,    calculated 

from  a   =  — — ,  varies,  while  K,  calculated  from  a   =  — 1LJL. 
Moo  Moo  ^oo 

is  a  constant. 

The  Object  of  This  Investigation. 

It  was  my  plan  in  this  work  to  study  the  relation  between 
the  dissociation  as  measured  by  the  freezing  point  and  con- 
ductivity methods;  to  determine  to  just  what  extent  the  con- 
ductivity of  a  solution  is  influenced  by  the  hydration  of  the 
ions;  and  to  study  the  effect  of  hydration  upon  the  relative 
velocities  of  different  ions. 

Moreover,  it  was  desired  to  test  the  reliability  of  the  conduc- 
tivity method  as  a  means  of  measuring  the  dissociation  of 
strong  electrolytes. 

In  order  to  do  this,  it  was  found  necessary  to  redetermine 
as  accurately  as  possible  the  freezing  point  lowerings  pro- 
duced by  various  solutions  of  a  large  number  of  salts. 

The  object  of  the  conductivity  measurements  was  to  deter- 
mine the  dissociation  of  the  solution  in  question,  as  accurately 
as  possible,  in  order  that  the  theoretical  lowering  produced 
by  the  substance,  if  there  was  no  hydration,  might  be  calcu- 
lated. 

The  freezing  point  measurements  give  us,  on  the  other  hand, 
an  exact  proportion  between  the  number  of  dissolved  parti- 
cles, molecules,  ions,  or  the  hydrates  of  these,  and  the  num- 
ber of  molecules  of  the  solvent  acting  as  such. 

EXPERIMENTAL. 

Freezing  Point  Apparatus. — For  all  concentrations  from 
the  most  dilute  up  to  those  which  could  not  be  frozen  by 
mixtures  of  salt  and  ice,  a  bath  of  rather  large  dimensions 
was  used.  The  outer  cylindrical  vessel  was  made  of  heavy 


22 

galvanized  iron — diameter  31  cm.,  depth  26  cm. — and  cov- 
ered on  the  outside  by  a  heavy  coat  of  felt  to  prevent  radia- 
tion. Within  this  was  a  much  smaller  vessel  of  the  same 
material  with  a  tightly  fitting  cover.  Soldered  around  the 
large  hole  in  the  center  of  the  cover  is  a  conical- shaped  collar, 
which  holds  firmly  the  cork  through  which  the  thermometer 
is  inserted.  By  this  means  the  thermometer  always  reaches 
to  the  same  depth  in  the  solution.  A  second  smaller  hole 
in  the  side  is  provided  for  the  passage  of  the  stirrer.  To  the 
bottom  and  on  the  outside  was  soldered  a  short  bolt,  which, 
in  turn,  was  screwed  into  a  nut  soldered  to  the  center  of  the 
outer  vessel.  In  this  way  firm  support  was  given  the  inner 
vessel  and  danger  of  floating  was  avoided.  The  freezing 
tube  proper  was  a  large  glass  tube — length  17  cm.,  diameter 
5.5  cm.,  and  of  250  cc.  capacity.  It  was  supported  within  the 
smaller  vessel  at  the  bottom  by  a  cork,  and  at  the  top  by  a 
cork  ring  which  rested  upon  an  iron  ledge  soldered  to  the 
inside  of  the  small  vessel.  These  dimensions  allowed  for  an 
air  space  of  about  2  cm.  all  around. 

The  stirrer  consisted  of  a  gold-plated  brass  disc  with  one 
large  hole  in  the  center  to  permit  the  passage  of  the  ther- 
mometer, and  around  this  smaller  holes  about  0.7  cm.  in  diam- 
eter. 

Near  the  top  of  the  large  outer  cylinder  was  soldered  a  small 
tube  which  served  to  keep  the  water  in  the  bath  at  constant 
level. 

By  means  of  a  bath  of  these  dimensions  the  temperature 
of  the  freezing  mixture  could  be  kept  constant  for  five  or  six 
hours.  No  attempt  was  made  to  control  exactly  the  tem- 
perature of  the  bath,  but  experience  taught  us  that  only  those 
freezing  mixtures  which  required  from  forty  seconds  to  one 
minute  to  cool  the  solution  o°.i  could  be  depended  upon  for 
reliable  results. 

For  solutions  requiring  freezing  mixtures  of  calcium  chloride, 
the  ordinary  cryoscopic  apparatus  consisting  of  a  battery 
jar,  two  test  tubes  were  used. 

For  this  work  4  thermometers  of  the  Beckmann  type  were 


23 

employed,  whose  temperature  ranges  were  i°.i,  5°.6,  i2°.2>, 
and  25°.  These  were  graduated  into  o°.oo2,  o°.oi,  o°.o2, 
and  o°.O5,  respectively  (whole  scale).  By  means  of  a  high- 
power  lens  it  was  easy  to  read  to  a  tenth  of  the  above  grad- 
uations. 

Conductivity. 

Apparatus. — The  conductivity  measurements  were  made 
by  means  of  the  well-known  Kohlrausch  method,  using  the 
Wheatstone  bridge,  induction  coil,  and  telephone  receiver. 
The  wire  was  calibrated  according  to  the  method  of  Strouhal 
and  Barus.1  The  resistance  coils  were  made  by  Leeds,  of 
Philadelphia,  and  had  been  carefully  calibrated. 

Conductivity  cells  of  two  types  were  used.  For  the  more 
dilute  solutions  cells  of  the  type  devised  by  Jones  and  Bing- 
ham2  were  employed.  For  the  more  concentrated  solutions 
U-shaped  cells,  similar  to  those  used  by  Jones  and  Getman,3 
were  found  to  be  very  convenient. 

All  conductivity  measurements  were  made  at  o°.  For 
this  purpose  a  small  pail  was  filled  with  finely  crushed  ice, 
moistened  with  distilled  water,  and  the  cells  packed  into  the 
ice  as  tightly  as  possible.  The  small  pail  was  then  placed 
in  a  spacious  pan  and  the  space  between  the  pail  and  the  pan 
filled  with  finely  crushed  ice. 

Specific  Gravity. 

Since  the  solutions  were  made  up  at  20°,  we  thought 
it  best  to  determine  their  specific  gravities  at  the  same 
temperature.  The  20°  bath  was  a  large  galvanized  iron  tub. 
By  means  of  a  very  small  flame  below  and  a  stirrer  within, 
driven  by  a  hot-air  motor,  the  temperature  could  easily  be 
kept  to  within  o°.i  of  the  desired  temperature.  Through- 
out this  work  six  pycnometers  of  the  Ostwald  type  were  em- 
ployed. They  were  carefully  calibrated  with  pure  redis- 
tilled water. 

1  Wied.  Ann.,  10,  326  (1880). 
»  Am.  Chem.  J.,  34,  481  (1905). 
«  Z.  physik.  Chem.,  46,  244  (1903). 


24 

Volumetric  Apparatus. 

The  flasks  and  burettes  used  in  this  work  were  carefully 
calibrated  at  20°  by  the  method  of  Morse  and  Blalock.1 

Solutions. 

Kahlbaum's  "chemically  pure"  materials  were  used  in  every 
case  and  were  further  purified  whenever  it  was  thought  desirable 
to  do  so.  The  method  of  preparing  the  solutions  varied 
according  to  the  solute  employed.  In  general,  a  solution  of 
slightly  greater  concentration  than  2  normal  was  first  made,  and 
from  this,  by  successive  dilutions,  the  lesser  concentrations 
were  obtained.  Whenever  possible,  the  mother  solution  was 
made  up  by  direct  weighing;  when  the  nature  of  the  solute 
did  not  permit  it  to  be  weighed,  the  mother  solution  was  di- 
luted to  convenient  strength,  and  portions  of  the  dilute  solu- 
tion were  standardized  either  by  gravimetric  or  volumetric 
methods. 

Water. 

The  water  which  was  used  in  all  the  solutions  was  puri- 
fied according  to  the  method  of  Jones  and  Mackay.2  Ordi- 
nary distilled  water  was  twice  redistilled  from  an  acidified 
solution  of  potassium  dichromate,  and  the  steam  from  the 
second  distillation  passed  through  a  boiling  solution  of  barium 
hydroxide.  It  had,  at  o°,  a  conductivity  of  about  1.2  X  lo""6 
to  1.7  X  io-7. 

Calculation  of  the  Composition  of  the  Hydrates. 

The  method  of  calculating  the  amount  of  water  combined 
with  the  dissolved  substance  is  essentially  the  same  as  that 
used  by  Jones  and  Bassett.3  We  have  given  the  observed 
molecular  lowering  of  the  freezing  point,  the  specific  gravity 
of  the  solutions,  and  the  dissociation.  The  observed  molecu- 
lar lowering  is  corrected  for  the  difference  between  1000  grams 
and  the  amount  of  water  actually  present  in  one  liter  of  the 

1  Am.  Chem.  J,,  16,  479  (1894). 

2  Ibid.,  19,  83  (1897). 

»  Ibid.,  33,  843  (1905);  34,  298  (1905). 


25 

solution.  This  gives  the  true  molecular  lowering  which  would 
be  produced  by  the  substance  at  the  dilution  in  question  if 
there  were  1000  grams  of  water  present. 

From  the  dissociation  we  calculate  the  true  molecular  low- 
ering which  would  be  produced  by  the  dissolved  substancs 
if  there  were  no  hydration ;  and  if  there  is  no  hydration  these 
two  values  for  the  molecular  lowering  should  be  equal. 

The  calculated  lowering,  divided  by  the  observed  lowering 
and  multiplied  by  1000,  gives  the  amount  of  water  present 
playing  the  r6le  of  solvent,  if  the  quantity  of  the  substance 
present  is  dissolved  in  1000  grams  of  water. 

The  difference  between  this  amount  of  water  and  1000 
grams  gives  the  amount  of  water  which  is  combined  with  the 
dissolved  substance  in  the  solution  in  question. 

Knowing  the  number  of  grams  of  water  which  are  in  com- 
bination with  the  dissolved  substance,  the  number  of  gram 
molecules  of  water  combined  with  the  substance  is  obtained 
by  dividing  this  number  by  18.  If  we  divide  this  value  by 
the  concentration  in  terms  of  normal,  we  obtain  the  number 
of  molecules  of  water  which  are  in  combination  with  one  mole- 
cule of  the  dissolved  substance  when  the  amount  of  sub- 
stance present  in  one  liter  of  the  solution  is  dissolved  in  1000 
grams  of  water. 

In  the  various  tables  of  data  the  symbols  have  the  following 
significance : 

In  the  tables  of  freezing  point  measurements  ra  is  the  con- 
centration in  terms  of  gram  molecules  per  liter ;  A,  the  ob- 
served lowering  of  the  freezing  point,  corrected  for  the  sepa- 
ration of  ice;  A/w,  the  molecular  lowering  of  the  freezing 
point. 

In  the  conductivity  tables,  V  denotes  the  volume  of  the  solu- 
tion in  liters  which  contains  one  gram  molecular  weight  of 
the  electrolyte;  y.  is  the  conductivity  corrected  for  water;  a 
is  the  approximate  dissociation. 

In  the  specific  gravity  tables,  m  is  the  concentration;  Wsolt 
the  weight  of  one  liter  of  the  solution ;  Wsalt  is  the  weight  of  the 
salt  contained  in  one  liter  of  the  solution ;  and  WHzO  is  the  weight 


26 

of  water  contained  in  one  liter  of  the  solution.  The  percent- 
age correction  is  the  correction  which  must  be  applied  to  the 
freezing  point  lowering  in  order  to  refer  it  to  1000  grams  of 
the  solvent  instead  of  the  amount  of  water  that  is  actually 
present  in  one  liter  of  the  solution  in  question. 

In  the  hydrate  tables,  m  is  the  concentration  in  gram  mole- 
cules per  liter;  a,  the  approximate  dissociation  as  measured 
by  the  conductivity  method;  L,  the  theoretical  molecular 
lowering  of  the  freezing  point  referred  to  1000  grams  of  sol- 
vent; A/m,  the  observed  molecular  lowering;  L',  the  corrected 
molecular  lowering ;  M,  the  number  of  gram  molecules  of  water 
in  combination  with  the  solute;  and  H,  the  number  of  gram 
molecules  of  water  combined  with  one  molecule  of  the  salt 
at  the  concentration  in  question. 

Calcium  Chloride. 

The  data  for  calcium  chloride  are  given  in  Tables  I.  to  IV. 

The  value  of  /IQO  is  surprisingly  low,  when  compared  with 
that  obtained  by  West1  and  by  Bassett.2  It  is,  however,  very 
nearly  equal  to  that  obtained  by  Jones  and  Stine.3 

A  study  of  Table  IV.  leads  us  to  the  following  conclusions: 
The  theoretical  molecular  lowerings,  as  given  in  column  L,  de- 
crease regularly  with  increase  in  concentration,  while  the  cor- 
rected observed  molecular  lowerings,  as  seen  in  column  L', 
decrease  rapidly,  reach  a  minimum  at  o.i  normal,  and  then 
increase  with  increase  in  concentration. 

It  is  very  probable  that  the  value  of  L'  for  o.oi  normal  is 
too  (large,  but  owing  to  the  inaccuracy  of  the  method  for 
such  dilutions,  this  is  unavoidable. 

It  will  be  seen  from  column  M  that  the  amount  of  water 
which  has  entered  into  combination  with  the  dissolved  salt 
also  passes  through  a  minimum  between  0.075  normal  and  o.io 
normal — the  same  concentration  which  gives  the  minimum 
molecular  lowering  of  the  freezing  point.  A  similar  minimum 

1  Am.  Chem.  J,,  34,  393  (1905). 

2  Ibid.,  33,  547  (1905). 

3  The  article  of  Jones  and  Stine  will  be  published   in  the  American  Chemica 
Journal  in  the  near  future. 


27 

was  noted  by  Jones  and  Bassett1  for  concentrations  ranging 
from  0.102  normal  to  0.153  normal.  It  has  been  assumed 
hitherto,  by  Jones  and  his  coworkers,  that  the  minimum  in 
the  freezing  point  lowering  always  occurs  in  that  concentra- 
ti  n  where  the  effect  due  to  decrease  in  dissociation  is  just 
counterbalanced  by  the  effect  due  to  hydration.  The  values 
of  L'  and  M  also  show  that  the  abnormality  of  the  freezing 
point  lowering  is  greatly  augmented  by  the  relatively  great 
hydrating  power  of  the  ions,  since  it  is  the  ions  with  which 
we  are  chiefly  concerned  in  the  dilute  solutions.  A  glance 
at  column  H  shows  us  at  once  the  great  hydrating  power  of 
the  ions  in  dilute  solution.  The  values  of  H  decrease  regu- 
larly with  increase  in  concentration  to  o.io  normal.  From 
that  concentration  on,  the  decrease  in  hydration  is  very  slight 
as  the  concentration  increases.  In  these  concentrations  the 
combined  effect  upon  the  freezing  point  lowering,  due  both 
to  the  dissociation  and  to  the  hydration  of  the  ions,  is  small, 
compared  with  the  effect  due  to  the  undissociated  molecules. 

If  we  refer  to  the  literature2  bearing  upon  the  relation  be- 
tween the  water  of  crystallization  of  a  salt  and  the  tempera- 
ture at  which  it  crystallizes,  we  see  that,  over  a  definite  range 
of  temperature,  the  amount  of  water  of  crystallization  is  con- 
stant. If,  then,  we  eliminate  the  hydration  due  to  the  ions, 
we  should  expect  to  find  the  number  of  molecules  of  water 
combined  with  one  molecule  of  the  salt  to  be  a  constant  for 
a  definite  range  of  temperature.  This  is  clearly  shown  by 
the  values  of  H  for  the  more  concentrated  solutions. 

The  values  of  M  are  plotted  in  the  curve  (Fig.  II.)  against 
the  concentrations  as  abscissas.  The  curve  shows,  at  a  glance, 
that  the  amount  of  water  held  in  combination,  from  the  dilu- 
tion at  which  the  minimum  occurs,  is  a  linear  function  of  the 
concentration. 

The  values  of  H  are  plotted  in  the  curve  (Fig.  I.)  against 
the  concentrations  as  abscissas.  An  explanation  regarding 

1  Am.  Chem,  J  ,  33,  548  (1905). 

2  Bassett:  Ibid.,  34,  294  (1905). 


28 


6.1     6-2$        6.5 


OJS     '  1. 

Concentration. 
Fig.  I. 


1.5 


these  hydrate  curves  is  necessary  at  this  point.  With  one 
or  two  exceptions,  it  was  found  impossible  to  plot  on  the  paper 
the  values  of  H  for  the  more  dilute  solutions. 

These  curves  show  the  rapid  decrease  in  hydration  until 
the  minimum  is  reached,  and  then  a  very  slight  decrease  with 
increasing  concentration. 


29 


20 


U    5.25      0.5 


D.75      1. 

Concentration. 
Fig.  II. 


L5 


Table  I. — Freezing  Point  Measurements. 


A. 


A/w. 


0.025 

•  vvJ7t«J 

0.1318 

o  •  7t«j^ 
5.2720 

2  .  8344 

91.72 

0.05 

0.2511 

5.0220 

2.7OOO 

85.00 

0.075 

0.3651 

4.8690 

2.6177 

80.88 

0.  10 

0.48515 

4-8515 

2.6083 

80.41 

0.25 

1-2335 

4-9340 

2.6526 

0.50 

2.6270 

5.2540 

2.8247 

0.75 

4.1955 

5  •  5940 

3.0075 

I.OO 

6  .  1040 

6.1040 

3.2817 

Table  II. — Conductivity  Measurements. 


V. 

100 

40 

20 

13-34 
10 


334 


I  .00 


0°  =   123.46. 


Ill .23 
104.66 

100. OI 

95-02 
92.23 
87.19 

80.73 
74.69 

70.98 


a. 


89.67 

84.37 
80.62 
76.60 

74-35 
70.62 

65-39 
60.49 

57-49 


Table  III.  —  Specific  Gravity 

Measurements. 

m.              Sp.  gr. 

Wsol. 

fl 

WH..O. 

Per  cent  of 
correction. 

0 

.01 

.000982 

1000.982 

i 

.109 

999.873 

0.012 

0 

.025 

.002539 

1002  .  539 

2 

.772 

999-767 

0.023 

0 

•05 

.  004874 

1004.874 

5 

•545 

999.329 

0.067 

0 

•  075 

.006814 

1006.814 

8 

.317 

998.497 

0.150 

0 

.10 

.008971 

1008.971 

n 

.090 

997.881 

O.2II 

0 

•25 

.02267 

1022.67 

27 

.725 

994-954 

0.504 

0 

•50 

[.04451 

1044.51 

55 

.450 

989.06 

1.094 

0 

.75         1.06641 

1066.41 

83 

.175 

983.23 

1.676 

I 

.00         1.08744 

1087.44 

i  10  .  900 

976.54 

2-345 

Table  IV .—Hydrates. 


m. 

a. 

L. 

A/i». 

L'. 

M. 

H. 

0.025 

84.37 

4.9885 

5.2720 

5-2708 

2.869 

114.7 

0.05 

80.62 

4-7590 

5.0220 

5-0187 

2.874 

57-4 

0.075 

76.60 

4.7095 

4  .  8690 

4.8617 

1.742 

23-2 

O.IO 

74-35 

4.6258 

4-8515 

4.8414 

2-474 

24-7 

0.25 

70.62 

4.487 

4-934 

4.910 

4.785 

19.1 

0-5 

65-39 

4-293 

5-254 

5-197 

9.663 

19.3 

0-75 

60.49 

4.  no 

5-594 

5-501 

14.048 

18.7 

I.OO 

57-49 

3.998 

6.104 

5-962 

18.30 

18.3 

Strontium  Chloride. 

The  concentrated  mother  solution  was  diluted  to  convenient 
strength  and  equal  portions  were  taken  for  standardization. 
The  strontium  was  precipitated  and  weighed  as  strontium 
carbonate. 

The  conductivity  measurements  for  this  salt  gave  me,  at 
maximum  dissociation,  /*oo  =  128.57.  The  corresponding 
value  obtained  by  Jones  and  Stine1  was  /too  =  128.44. 

The  minimum  in  the  freezing  point  lowerings  (column  L') 
is  found  at  0.25  normal,  whereas  the  minimum  in  the  total 
combined  water  occurs  at  a  somewhat  greater  dilution  (0.05 
normal).  The  values  of  H  become  approximately  constant 
at  0.25  normal,  the  minimum  point  in  the  freezing  point 
lowering. 

The  values  of  m  and  H  for  calcium  and  strontium  chlorides 
Tables  IV.  and  VIII.,  show  numbers  of  approximately  the 
same  order  of  magnitude.  For  curves,  see  Figs.  I.  and  II. 

1  Loc.  tit. 


Table  V. — Freezing  Point  Measurements. 


m. 

o.oi 
0.02937 
0.03987 
0.5011 
0.7077 

O.  10 

0.25 
0.50 
0.75 

1. 00 


0.05273 
0.1550 
0.2026 
0.2476 

0.3472 

o . 48904 

1-1957 
2.5339 
4.0989 
5.9211 


2730 
2800 


5 
5 
5-0752 

4-9349 
4 . 9060 
4.8904 
4.7830 
5-0678 
5-4652 
5.9211 


^. 

2-8351 
2.8386 
2.7382 
2.6531 
2.6376 
2.6292 
2.5715 
2-7354 
2.9385 
3.1833 


91.87 

91.93 
86.91 

82.65 
81.88 
81.46 
78.57 


Table  VI.  —  Conductivity  Measurements. 

^00   0°    = 

128.57  (Stine  128.4). 

V. 

HV. 

a. 

IIOO 

128.57 

SSO 

\J  / 

127.99 

\j  \J 

100 

115.64 

89.37 

34-04 

106.  10 

82.56 

25.08 

103.26 

80.32 

19.93 

101  .04 

78.08 

14.03 

98.06 

76.27 

10 

95.98 

74.17 

4 

88.07 

68.59 

2 

82.18 

63.96 

1-333 

74-86 

58.30 

1.0 

71.23 

55-47 

Table  VII.  —  Specific  Gravity  Measurements. 

m.       Sp.  gr. 

Wsol. 

Wsalt.       Wl 

.  _   Per  cent  of 
*•**   correction. 

0 

.01 

.0012284 

1001 

2284 

I 

•585 

999- 

7034 

0 

.029 

0 

•02937 

.0038396 

1003 

8396 

4 

•6559 

999- 

2837 

0 

.071 

0 

.03987 

.0053832 

1005 

3832 

6 

•3197 

999- 

0635 

0 

.093 

0 

.05017 

.007028 

1007 

028 

7 

.952 

999. 

078 

0 

.092 

0 

.07077 

.00956 

1009 

516 

ii 

.217 

998. 

299 

0 

.170 

0 

.  IO 

.013205 

1013 

215 

15 

•85 

997- 

930 

0 

.207 

0 

.25 

•034433 

1034 

433 

38 

.625 

994- 

808 

0 

.519 

0 

.5 

.068379 

1068 

379 

79 

•  250 

989- 

129 

I 

.087 

0 

.75  .5 

.  101760 

IIOI 

1  60 

118 

.875 

982. 

885 

I 

.711 

I 

.00    ] 

.135423 

1135 

423 

158 

•50 

976. 

923 

2 

'308 

32 

Table  VIII. —Hydrates, 
a.  L.  A/w.  L> '.  M.  H. 


0.01 

89. 

37 

5 

.1845 

5 

-2733 

5 

.2718 

.  .  .  . 



0.02937 

82. 

56 

4 

.9312 

5 

.2800 

5 

•  2763 

3 

•634 

123.6 

0.03987 

80. 

32 

4 

.8479 

5 

-0752 

5 

.0705 

2 

-439 

61.2 

0.05017 

78. 

08 

4 

.7645 

4 

•9349 

4 

.9304 

I 

.871 

37-2 

0.07077 

76. 

27 

4 

.6982 

4 

.9060 

4 

•8977 

2 

•274 

32-13 

O.  IO 

74. 

17 

4 

.6191 

4 

.8904 

4 

.8803 

2 

•973 

29-73 

0.25 

68. 

59 

4 

.4115 

4 

.7830 

4 

.7582 

4 

•047 

16.18 

0.50 

63. 

96 

4 

•2393 

5 

.0678 

5 

.0127 

8 

.572 

17.14 

0.75 

58. 

30 

4 

.0287 

5 

.4652 

5 

-37I8 

13 

.890 

18.52 

I.OO 

55- 

47 

3 

•9234 

5 

.9211 

5 

•7844 

17 

.873 

17.87 

As  in  the  case  of  calcium  chloride,  the  values  of  the  theo- 
retical lowerings  (L)  are  less  than  the  observed  lowerings  (L;) 
in  every  instance. 

Magnesium  Chloride. 

The  value  of  /*oo  for  magnesium  chloride  was  found  to  be 
123.95.  The  values  of  U  show  a  minimum  at  0.25  normal, 
while  the  values  of  H  begin  to  be  constant  at  0.5  normal. 
Magnesium  chloride  differs  from  the  other  chlorides  thus  far 
discussed  in  that  its  values  for  M  show  no  minimum,  but  in- 
crease regularly  with  increasing  concentration. 

It  should  be  noticed  also  that  magnesium  chloride  has  greater 
power  to  combine  with  water  than  any  of  the  halides  of  the 
calcium  group.  Especially  is  this  the  case  in  the  dilute  solu- 
tions, where  the  ions  predominate.  That  this  is  not  due  to 
hydrolysis  and  the  liberation  of  the  free  mineral  acid  is  evi- 
dent from  the  fact  that  the  molecular  lowering  of  the  freezing 
point  in  the  dilute  solutions  is  in  every  case  considerably 
higher  than  the  calculated  lowering.  As  we  shall  see  later, 
in  our  study  of  the  acids  just  the  reverse  was  found  to  be 
the  case.  The  curves  for  this  salt  are  found  in  Figs.  I.  and  II 


33 


Table  IX. — Freezing  Point  Measurements. 


m. 

A. 

0.004928 

0.02741 

0.007317 

0.04072 

O.OI 

0.05472 

0.05108 

0.2678 

0.07171 

0.3687 

0.09986 

0.5133 

0.25 

1.2352 

0.50 

2  .  6768 

0.75 

4.4328 

0.9415 

6.O6I9 

A/w. 
5.5630 


5.4720 

5.2443 
5.1421 

1330 
9408 
3536 
9104 


6.4885 


2.9909 
2.9916 
2 . 9420 
2.8195 
2.7651 
2.7596 
2.6563 
2.8783 
3.1776 
3.4615 


99-54 

97.10 

90.75 
88.25 
87.68 
82.81 


Table  X. — Conductivity  Measurements. 


V. 


402.25 
202 . 92 
136.67 

100. 0 

32.21 
19.57 
13.94 

10. O 

4.0 

2.0 

1-333 
1.062 


o°  =  123.95, 

V-v. 

120.15 
II6.67 
113.86 

112.68 

103.08 

98.88 

95.36 
91.25 
80.22 
72.07 
64.69 
60.31 


a. 
96.94 

94-13 
91.86 
90.90 
83-16 
79-78 
76.93 
73-61 
64.72 
59-50 
53.63 
48.66 


Table  XI. — Specific  Gravity  Measurements. 


m.                    Sp.  gr. 

Wsol. 

Wsalt. 

!//„.  _       Per  cent  of 
WH^O.      correction. 

0 

.00493     1.000344 

1000 

•344 

O. 

4695 

999.875 

0 

.OI2 

0 

.007327    1.000524 

IOOO 

•524 

O. 

6970 

999.827 

0 

.017 

0 

.01             1.000842 

IOOO 

.842 

0. 

9526 

999.889 

O 

.012 

0 

.03104      1.002756 

IOO2 

•756 

2. 

9568 

999.799 

O 

.O2O 

0 

.05108      ] 

.004224 

1004 

.224 

4. 

9168 

999.307 

0 

.069 

O 

.07171 

.  006036 

IOO6 

.036 

6. 

8316 

999-204 

0 

.079 

0 

.100 

•008505 

1008 

•505 

9- 

5260 

998.979 

O 

.102 

O 

.25 

.020966 

I02O 

.966 

23- 

8150 

997.151 

0 

.284 

0 

.50 

.038496 

1038 

.496 

47- 

630 

990.866 

O 

.9IO 

0 

•75 

.056905 

1056 

.905 

7i. 

445 

985.460 

I 

•450 

0 

.9415      & 

.069617 

IO69 

.617 

89. 

689 

979-930 

2 

.007 

34 
Table  XIL— Hydrates. 


m. 

a. 

L. 

A/fii. 

L'. 

M. 

H. 

O.OI 

90.90 

5.2415 

5.4720 

5.47H 

2-334 

233.4 

0.03104 

83-16 

4.9535 

5.3581 

5.3570 

4-I85 

134.82 

0.05108 

79.78 

4.8278 

5  .  2443 

5.2407 

4-377 

85.69 

0.07171 

76.93 

4.7218 

5.1421 

5-1381 

4-501 

62.76 

O.IO 

73.61 

4.5982 

5.I330 

5.1278 

5.737 

57-37 

0.25 

64.72 

4-1675 

4  .  9408 

4.9268 

8.562 

34.24 

0.50 

59-50 

4-0734 

5.3536 

5.3049 

12.898 

25.79 

0.75 

53.63 

3.8550 

5-9104 

5-8247 

18.787 

25.05 

0.9415 

48.66 

3.670I 

6.4385 

6.3098 

23.242 

24.68 

Barium  Chloride. 

A  nearly  saturated  solution  of  this  salt  was  first  made. 
This  was  diluted  to  convenient  concentration,  and  equal  por- 
tions were  precipitated  and  weighed  as  barium  sulphate. 
Owing  to  the  slight  solubility  of  this  salt,  we  did  not  attempt 
to  work  with  concentrations  greater  than  0.4  normal. 

Conductivity  measurements  gave  us  the  value  P&  —  132.07. 


Table  XIII. — Freezing  Point  Measurements. 


m. 

O.OI 

0.025 

0.05 

0.075 

O.IO 

0.25 


0.40 


A. 

0.5463 

L3398 

0.24770 

0.36128 

0.4792 

I . 1669 

1.902 


A/w. 
5.4630 
5.3592 
4.9551 
4.8171 

4.7925 
4.6677 

4-7370 


2.9370 
2.8813 
2.6639 
2 . 5898 
2.5766 
2 • 5095 
2-5575 


96.85 
94.06 

83.19 
79-49 
78.83 

75-47 


Table  XIV. — Conductivity  Measurements. 

/*oo  °°  =  132.07. 

V.  *,.  a. 

100  120.01  90.87 

40  HI.I5  84.16 

20  105.78  80.09 

13.33  100.69  76.24 

10  99.92  75.65 

4  92.18  69.79 

2.5        86.31  65.35 


35 


Table  XV. — Specific  Gravity  Measurements 


tn. 

Sp.  gr. 

Wsol. 

Wsalt. 

WH&. 

Per  cent  of 
correction. 

O.OI 

.001878 

1001.87 

2.083 

999  795 

O.O2I 

0.025 

•00475 

1004.75 

5.207 

999-545 

0.045 

0.05 

.00929 

1009  .  29 

10.415 

998.879 

O.  112 

0.75 

•01369 

1013.69 

15.622 

998.074 

0.197 

O.  IO 

.01766 

1017.66 

20.830 

996.83 

0.3l6 

0.25 

.0456 

1045.61 

52.075 

993-542 

0.645 

0.40 

.0726 

1072.65 

83.32 

989.335 

I  .066 

Table  XV I. —Hydrates. 


m. 

a. 

L. 

k 

\/nt. 

L'. 

JJf. 

H. 

0.025 

84. 

16 

4- 

9907 

5- 

3592 

5- 

3568 

3-796 

I5I.8 

0.05 

80. 

09 

4- 

8393 

A 

9551 

4- 

9496 

i. 

238 

24.7 

0.075 

76. 

24 

4- 

6961 

4 

,8171 

4- 

8080 

i. 

293 

17.2 

O.IO 

75- 

65 

4- 

6742 

4 

7925 

4- 

7772 

I. 

197 

H-9 

0.25 

69. 

79 

4- 

4562 

4 

6677 

4- 

6374 

2. 

172 

8.69 

0.40 

65- 

35 

4- 

2910 

4, 

7570 

4- 

7061 

4- 

900 

12.25 

What  has  been  said  regarding  the  chlorides  of  calcium, 
strontium,  and  magnesium  applies  equally  well  to  barium 
chloride.  The  low  value  of  H  for  0.25  normal  is  doubtless 
due  to  experimental  error. 

It  is  interesting  to  note  that  while  the  molecules  of  barium 
chloride  have  a  much  smaller  hydrating  power  than  the  other 
chlorides  of  the  alkaline  earth  metals,  as  we  should  expect 
from  the  fact  that  it  crystallizes  with  but  two  molecules  of 
water,  the  ions  which  predominate  in  the  dilute  solutions 
have  a  relatively  high  hydrating  power. 

Another  point  is  to  be  noted,  one  to  which  reference 
will  be  made  later  in  this  paper.  A  glance  at  the  curves  rep- 
resenting the  values  of  M  and  H  for  the  three  salts — calcium, 
strontium,  and  magnesium  chlorides — will  show  that  in  each 
case  the  curves  for  calcium  chloride  lie  above  those  for  stron- 
tium chloride,  while  the  two  curves  for  magnesium  chloride  lie 
above  those  for  calcium  chloride.  This  order  is  just  the  re- 
verse of  that  for  the  atomic  volumes  of  the  three  metals.  Al- 
though barium  chloride  crystallizes  with  but  two  molecules 
of  water,  the  atomic  volume  of  barium  is  still  larger  than 
that  of  strontium.  This  may  account  for  the  relatively  high 
hydrating  power  of  the  ions  of  barium  salts. 


36 

The  curves  for  the  values  of  M  and  H  are  given  in  Figs. 
II.  and  I.,  respectively. 

Calcium  Nitrate. 

The  mother  solution  was  diluted  and  50  cc.  portions  were 
taken  for  standardization.  The  calcium  was  precipitated 
by  means  of  ammonium  oxalate  and  weighed  as  calcium 
oxide.  The  data  are  given  in  Tables  XVII.  to  XX. ;  the  curves 
are  plotted  in  Figs.  III.  and  IV. 


70 


41    1.25 


1  S 


Concentration. 
Fig.  III. 


37 


Table  XVII. — Freezing  Point  Measurements. 


m. 

A. 

A/m. 

i. 

a. 

OOI2  ^ 

0.072 

c  .  7560 

•  *-'  A  ^  O 

0.025 

0.1303 

O  •  /  O*"" 

5.2120 

2  .  802  I 

90.10 

0.05 

o  .  2405 

4.8090 

2.5855 

79.27 

0.125 

0.5752 

4.6019 

2.4736 

73.68 

0.25 

I  .  1424 

4.5695 

2.4567 

72.83 

0.5 

2.2860 

4.5720 

2.4580 

0.75 

3.484 

4.645 

2-4974 

I.O 

4.766 

4.766 

2.5623 

1-5 

7.616 

5.077 

2.7299 

V. 


Table  XVIII. — Conductivity  Measurements. 
/KOO  o°  =  126.69. 

Hv.  a 


0.8o 
0.40 
O.2O 

8.0 
o 
o 

333 
o 


0.6667 


108.60 

IO2 . 78 
96.28 
85.72 
77.64 
66-54 
58.32 
51.30 
40.24 


85.72 
8I.I3 
76.0O 
67.66 
61.28 
52.52 
46.03 

40.49 
31-75 


38 
Table  XIX. — Specific  Gravity  Measurements. 


m. 

Sp.  gr. 

Wsoi. 

WsaU.     WH*0. 

Per  cent  of 
correction. 

o 

.0125 

i 

.001846 

1001 

.846 

2 

.052 

999- 

794 

0 

.021 

0 

.025 

i 

.003166 

1003 

.166 

4 

.104 

999 

062 

O 

•094 

0 

•05 

i 

.00604 

1006 

.04 

8 

.209 

997 

831 

O 

.217 

0 

•125 

i 

•01523 

1015 

.23 

20 

.520 

994 

71 

o 

•529 

0 

•25 

i 

.03074 

1030 

•74 

41 

.04 

989 

70 

I 

•03 

0 

•5 

i 

.06011 

1060 

.  ii 

82 

.09 

978 

02 

2 

.198 

0 

•75 

i 

.08874 

1008 

•74 

123 

•13 

965 

61 

3 

•439 

I 

.00 

i 

.11751 

1117 

.51 

164 

.18 

953 

33 

4 

.66 

I 

•5 

i 

•17375 

1173 

•75 

246 

•27 

927 

48 

7 

•25 

Table  XX.— Hydrates. 

m.  a.  L.  A/w.  Lf .  M.  H. 

0.025      81.13       4.8780       5.2120       5.2072       3.511      140.4 


0.05 

76.00 

4.6872 

4  .  8090 

4.7986 

1.288 

25-7 

0.125 

67.66 

4-3769 

4.6019 

4-5776 

2.437 

19.5 

0.25 

61.28 

4-139 

4-569 

4-522 

4.703 

18.8 

0.5 

52.52 

3-813 

4-572 

4.471 

8.173 

16.3 

0.75 

46.03 

3-572 

4-645 

4-485 

11.312 

15.07 

I.OO 

40.49 

3.366 

4.766 

4-544 

14.490 

14.49 

i-5 

31-75 

3-041 

5-077 

4.709 

19.683 

13.12 

Nothing  special  need  be  said  regarding  the  data  for  this 
salt,  except  to  call  attention  to  the  fact  that  the  amounts  of 
water  combined  with  calcium  chloride  in  solution  are,  in 
general,  higher  than  the  amounts  combined  with  calcium  ni- 
trate. This  is  just  what  we  should  expect  when  we  consider 
that  calcium  chloride  crystallizes  with  6  molecules  of  water, 
while  calcium  nitrate  crystallizes  with  4. 

Strontium  Nitrate. 

The  strontium  was  precipitated  and  weighed  as  the  car- 
bonate. Unlike  the  other  salts  thus  far  studied,  the  freezing 
point  lowerings  show  no  minimum  within  the  range  of  con- 
centrations used,  the  molecular  lowering  constantly  decreas- 
ing in  value.  A  minimum  was,  however,  obtained  by  Jones 
and  Bassett1  at  a  concentration  of  about  1.5  normal. 

i  Am.  Chem.  J.,  34,  305  (1905). 


39 
Table  XXL — Freezing  Point  Measurements. 


m. 

A. 

A/w. 

i. 

a. 

O.OI 

0.05717 

5.7170 

3.0736 

103.68 

0.025 

0.1304 

5.2180 

2.8053 

90.27 

0.05 

o  .  2402 

4-8050 

2.5833 

79.16 

0.075 

0.3492 

4.6567 

2.5036 

75-iS 

O.IO 

0.4587 

4.5875 

2.4664 

73-32 

0.25 

I.08I7 

4.326 

2.3263 

66.31 

0.5 

2.0849 

4.169 

2.2418 

62.09 

0.75 

3.0453 

4.060 

2.  1829 

59-15 

I.OO 

3.9983 

2.1496 

57.48 

Table  XXII.— 

Conductivity 

Measurements. 

/*oo    °°   ==   125.62. 

V. 

Hv. 

a. 

IOO 

III.I4 

88.47 

40 

100.95 

80.36 

20 

94.12 

74.92 

13 

•34 

89.26 

71.06 

IO 

86.16 

68.59 

4 

73-59 

58.58 

2 

61.34 

48.83 

I 

•33 

52.77 

42.01 

I 

45.69 

36.37 

Table  XXIII. — Specific  Gravity  Measurements. 


m.      Sp.  gr.      Wsoi. 

Wtalt.    Wl 

,  _   Per  cent  of 
**u'   correction. 

o.oi    1.001525 

1001 

.525 

2 

.116 

999 

.409 

0 

.059 

O 

.025   1.004207 

1004 

.207 

5 

.292 

998 

.915 

0 

.108 

0 

.05 

.008391 

1008 

.391 

IO 

.584 

997 

.807 

0 

.219 

0 

•075 

.012646 

IOI2 

.646 

15 

.876 

996 

•77 

o 

•323 

0 

.  IO 

.016834 

1016 

•  834 

21 

.168 

995 

.666 

0 

-433 

0 

.25 

.04201 

1042 

.01 

52 

.92 

989 

•09 

I 

.09 

0 

.5 

.08312 

1088 

.  12 

105 

.84 

977 

.28 

2 

.27 

0 

.75 

.12386 

1123 

.86 

158 

.76 

965 

.11 

3 

.48 

I 

.00 

•  16354 

1163 

.54 

211 

.68 

95i 

.86 

4 

.814 

40 

Table  XXIV  .—Hydrates. 

m.  a.  L.  A/w.  L> '.  M.  H. 

0.025      80.36     4-8493       5-7i8o       5-7I24       3-870       154-8 


0.05 

74.92 

4.6470 

4  .  8050 

4-7945 

1.710 

34.20 

0.075 

71.06 

4-5034 

4.6567 

4.6418 

1-657 

22.09 

O.IO 

68.59 

4-4115 

4-5875 

4-5677 

1.900 

19.00 

0.25 

58.58 

4.0391 

4.3269 

4.2798 

3.124 

12.49 

0.5 

48.83 

3.676 

4.169 

4-075 

5-437 

10.87 

0.75 

42.01 

3.422 

4.060 

3.9i8 

7-030 

9.37 

1.  00 

36.37 

3-213 

3-998 

3.806 

8.607 

8.65 

The  values  for  the  combined  water  show  a  minimum  at  0.075 
normal,  just  as  calcium  nitrate  does. 

The  hydration  per  ion  and  molecule  also  shows  no  tendency 
to  become  constant. 

The  curves  are  plotted  in  Figs.  III.  and  IV. 

Magnesium  Nitrate. 

The  nitrate  of  magnesium,  like  the  chloride,  shows  a  much 
greater  power  to  combine  with  water,  throughout  the  range 
of  concentration  studied,  than  do  the  nitrates  of  the  alkali 
earth  metals. 

Table  XXV. — Freezing  Point  Measurements. 


m. 

A. 

A/w. 

i. 

a. 

0.02 

O.IO78 

5-3903 

2  .  8980 

94.90 

0.05 

0.24968 

4-9938 

2.6848 

84-24 

O.IO 

0.49085 

4.9085 

2.6390 

81-95 

0.15 

o  .  74486 

4.9671 

2.6705 

83.52 

O.2O 

0.99875 

4-9937 

2.6848 

0.50 

2  .  74280 

5-4856 

2.9492 

1.  00 

6.5H5 

6.5H5 

3.5024 

Table  XXVI. — Conductivity  Measurements. 

/KOO  o°  =  119.90. 

V.                                       PV.  a. 

50                                    102.06  85.12 

20                                                 94.48  78.80 

10                               89.66  74.78 

6.666                           85.61  71.40 

5                                   83.04  69.25 

2                                   72.03  60.07 

I                                   59-27  49-43 


4i 
Table  XXVII.  —  Specific  Gravity  Measurements. 

m.               Sp.  gr. 

W50l. 

malt.          Wi 

Per  cent  of 
/jG>.      correction. 

O 

.02         1.00224 

1002.224 

2 

.968 

999 

•255 

0 

.074 

0 

.05        I  .  005626 

1005.626 

7 

.422 

998 

.204 

0 

•179 

0 

.  IO 

.011118 

1011.118 

H 

.844 

996 

.274 

0 

•372 

0 

.15 

•016557 

1016.557 

22 

.266 

994 

.291 

0 

•571 

0 

.20 

.022026 

1022.026 

29 

.688 

992 

.338 

0 

.766 

0 

•  50 

.  054804 

1054.804 

74 

.220 

980 

.584 

I 

.941 

I 

.00 

.  107865 

1107.865 

148 

.440 

959 

•425 

4 

•057 

I 

.274 

.136615 

1136.615 

189 

.  112 

947 

•502 

5 

.249 

Table  XXVIII. 

Hydrates. 

m. 

a. 

L. 

A/w. 

L'. 

M. 

H. 

0.05 

78. 

,80 

4 

•7913 

4- 

9938 

4 

.9849 

2 

.157 

43-14 

O.  10 

74 

,78 

4 

.6418 

4- 

9085 

4 

.8903 

2 

.817 

28.17 

0.15 

7i 

40 

4 

.5161 

4- 

9671 

4 

.9388 

4 

•759 

31-73 

O.20 

69 

25 

4 

.4361 

4- 

9937 

4 

•9555 

5 

.819 

29.09 

0.50 

60 

07 

4 

.0946 

5- 

4856 

5 

•3792 

13 

.260 

26.52 

I.  00 

49 

43 

3 

.6988 

6. 

5H5 

6 

.2507 

22 

.672 

22.67 

1.274 

44. 

46 

3 

•5139 

7- 

1032 

6 

•7303 

29 

.006 

22.76 

The  amount  of  water  decreases  with  increase  in  concentra- 
tion in  the  dilute  solutions,  reaches  a  minimum  at  0.05  to 
0.075  normal,  and  then  increases  regularly  with  increase  in 
concentration. 

The  values  of  H  do  not  approach  a  constant  until  normal 
concentration  is  reached. 

It  is  very  probable  that  the  relatively  low  values  of  H  for 
0.05  and  o.i  normal  are  due  to  errors  in  measuring  the  freez- 
ing points  of  those  solutions. 

The  curves  for  magnesium  nitrate  are  given  in  Figs.  III. 
and  IV. 

Barium  Nitrate. 

Owing  to  the  very  small  solubility  of  this  salt  I  did  not  at- 
tempt to  make  measurements  beyond  0.15  normal.  Barium 
nitrate  has  special  interest  in  that  it  is  the  first  salt  thus  far 
studied  in  this  investigation  which,  under  ordinary  condi- 
tions, crystallizes  without  water. 


42 

Table  XXIX. — Freezing  Point  Measurements. 


m. 

A. 

A/I*. 

i. 

«. 

O.OI 

0.05545 

5-5450 

2.9812 

99.06 

0.025 

0.12482 

4.9928 

2.6838 

84.19 

0.05 

0.23281 

4-6566 

2  •  5035 

75-18 

0.075 

0.32704 

4  •  3606 

2  .  3440 

67.20 

O.  IO 

O.420I8 

4.2018 

2.2590 

62.95 

0.15 

0-59935 

3-9955 

2.1481 

57-40 

Table  XXX. — Conductivity  Measurements. 

/AGO  o°  =  128.08. 
V.  PV.  a. 

loo  110.62  86.37 

40  99.04  77.32 

20  90.26  70.47 

13.34  83.92  65.51 

10  78.59  61.36 

6.67  71.05  55.47 

Table  XXXI. — Specific  Gravity  Measurements. 


m. 

Sp.  gr. 

Wsoi.     Wsait.     WH^O- 

Per  cent  of 
correction. 

O 

.01 

I 

.OO2O3I 

1002 

.031 

2 

.14 

999 

.891 

O 

.088 

0 

.025 

I 

.005224 

1005 

.224 

6 

•537 

998 

.687 

0 

•  131 

0 

.05 

I 

.010591 

1010 

•591 

13 

.074 

997 

.517 

0 

.248 

0 

.075 

I 

.015671 

1015 

.67I 

19 

.611 

996 

.060 

0 

.394 

0 

.10 

I 

.021143 

102  1 

•143 

26 

.148 

994 

-995 

0 

.500 

0 

.15 

I 

.031770 

1031 

•770 

39 

.222 

992 

.548 

0 

•745 

Table  XXXII.— Hydrates. 


m.      a. 

L. 

A/w. 

L'. 

M. 

H. 

0.05 

70 

•47 

4 

4814 

4 

.6566 

4 

.6451 

I  . 

957 

39.15 

0.075 

65 

.51 

4 

2969 

4 

.3606 

4 

•3434 

o. 

595 

7.93 

O.IO 

61 

•30 

4 

1425 

4 

.2018 

4 

.1808 

0 

509 

5-09 

O.IO 

55 

•47 

O  ' 

9234 

3 

•9955 

3 

.9648 

0, 

5805 

3-87 

It  will  be  seen  that,  like  strontium  nitrate,  the  molecular 
lowering  of  the  freezing  point  decreases  regularly  as  the  con- 
centration increases,  without  showing  a  minimum  value. 

The  amount  of  water  held  in  combination  decreases  rapidly 
and  reaches  a  minimum  at  o.i  normal. 

The  hydration  per  molecule  is  very  small,  as  we  should  ex- 
pect, since  the  salt  in  its  solid  state  is  anhydrous.  In  the 
more  dilute  solutions,  however,  where  the  ions  predominate, 
the  hydration  is  of  the  same  order  as  that  of  the  other  nitrates 
of  the  alkali  earths. 


"\>  "*•        ^K 

OF  THE  \ 

UNIVERSITY   J 


43 

This  is,  indeed,  convincing  proof  that  the  ions  themselves 
have  great  hydrating  power. 

It  was  pointed  out  in  the  introduction  that  if  there  were 
no  hydration  the  corrected  molecular  lowering  of  the  freezing 
point  should  be  equal  to  the  corrected  lowering.  A  glance 
at  Table  XXXII.  will  show  how  closely  the  assumption  agrees 
with  facts.  The  values  for  the  corrected  freezing  point  low- 
erings  for  the  three  most  concentrated  solutions,  in  which  the 
hydration  is  least,  are  only  about  one  per  cent  higher  than  the 
calculated  values.  Moreover,  if  there  is  no  hydration  and 
if  we  may  disregard  the  effect  of  viscosity  upon  the  velocity 
of  the  ions,  we  should  expect  the  dissociation  as  measured  by 
the  conductivity  and  freezing  point  methods  to  be  the  same. 
That  this  is  true  may  be  seen  by  consulting  the  values  of  a 
for  0.075,  o.io,  and  0.25  normal  in  Tables  XXIX.  and  XXX. 
Owing  to  slight  hydration,  the  amounts  of  dissociation,  as 
measured  by  the  freezing  point  method,  are  slightly  higher 
than  those  measured  by  the  conductivity  method. 

The  curves  for  barium  nitrate  are  given  in  Figs.  III.  and 
IV. 

Since  the  two  barium  salts  studied  are  so  slightly  soluble, 
it  was  thought  best  to  add  the  tables  for  the  hydrates  of  bar- 
ium bromide  and  barium  iodide  which  were  prepared  by 
Jones  and  Bassett.1  Both  of  these  salts  crystallize  with  two 
molecules  of  water  of  crystallization. 


Table  XXXIII.  —Hydrates. 

m. 

«. 

L. 

A/ra. 

L1. 

M. 

H. 

O.  10 

79-3 

4.81 

5.06 

5-04 

2-54 

25.4 

0.15 

77-7 

4-75 

4.91 

4.88 

1.48 

9-9 

0.25 

73-8 

4.60 

5-oo 

4.96 

4-03 

16.1 

0.40 

71-3 

4-52 

5-09 

5-03 

5.63 

14.1 

0.50 

68.8 

4.42 

5.  18 

5-09 

6.22 

12.5 

0.6774 

65-3 

4.29 

5-74 

5-59 

12.92 

19.1 

0.9032 

64.8 

4.27 

5-87 

5  66 

13.64 

15-1 

I.  1290 

61.1 

4-13 

6.24 

5-93 

16.88 

14.9 

I  •  3548 

58.4 

4-03 

6.66 

6.28 

19.90 

14.7 

1.5806 

55-6 

3-93 

7.12 

6.63 

22.66 

14-3 

1.884 

50.90 

3-75 

7.67 

7.06 

26.05 

14.4 

2.258 

41.1 

3-39 

8-343 

7-58 

30.71 

13-6 

i  Am,  Chem.  J.,  33,  553  (1905);  34,  306  (1905). 


44 
Table  XXXIV.— Hydrates. 


m. 

a. 

L. 

A/m. 

L'. 

M. 

H. 

0.076 

78.6 

4.78 

4.92 

4.91 

1-47 

19.3 

0.153 

75-9 

4.68 

5.00 

4.96 

3-14 

20.5 

0.306 

74-9 

4.65 

5-17 

5-o8 

4.70 

15-4 

0.612 

71.0 

4-54 

6.08 

5-86 

12.51 

20.4 

0.917 

64.8 

4-27 

6.69 

6.29 

17.84 

19-5 

I  .222 

6k.  i 

4  13 

7-54 

6.98 

22.70 

18.1 

1.528 

55-5 

3-92 

8.67 

7-83 

27.74 

18.2 

1.834 

51.1 

3-76 

9.54 

8-44 

31.92 

17.4 

2.139          45.0         3.53          11.22          9.67         35-28          16.5 

The  solubilities  of  these  two  salts  are  nearly  equal  to  that 
of  the  other  halides  of  the  calcium  group.  It  is  very  probable, 
owing  to  the  fact  that  Jones  and  Bassett  used  a  thermometer  less 
sensitive  than  the  one  employed  in  this  work,  that  the  observed 
freezing  point  lowerings  for  the  most  dilute  solutions  are  too  low. 
This  would,  of  necessity,  give  low  values  for  the  total  com- 
bined water  and  for  the  hydration. 

The  values  of  M  for  these  salts  increases  regularly  with 
increase  in  concentration.  The  magnitude  of  hydration 
for  each  salt  is  approximately  constant.  If  we  compare  the 
values  of  H  for  the  four  barium  salts  in  Tables  XVI.,  XXXII., 
XXXIII.,  and  XXXIV.,  we  see  that  of  the  halides  the  iodide  has 
the  greatest  hydrating  power,  and  the  chloride  the  least,  while 
the  bromide  stands  intermediate  between  the  other  two. 
The  nitrate  has  the  least  hydrating  power. 

Since  the  chloride,  bromide,  and  iodide  crystallize  each  with 
two  molecules  of  water,  we  should  expect  the  observed  molec- 
ular lowering  to  be  greater  than  the  calculated.  Experimen- 
tal results  confirm  this. 

Cobalt  Chloride. 

An  approximately  two  normal  solution  was  first  made 
up.  A  portion  of  this  was  diluted  to  convenient  strength, 
and  the  cobalt  determined  electrolytically. 

Cobalt  chloride  crystallizes  with  6  molecules  of  water,  and, 
like  the  other  chlorides  with  the  same  amount  of  water  of 
crystallization,  has  a  large  hydrating  power.  The  results  are 
just  what  we  should  expect. 


45 
Table  XXXV. — Freezing  Point  Measurements. 


m. 

A. 

A/w. 

i. 

a. 

O.OI 

0.06241 

6  24.1 

0.025 

0.1394 

vy  .  •^f-*- 
5-5786 

2.9992 

99.96 

0.05 

o  .  2609 

5.2186 

2.8057 

90.28 

0.075 

0.3356 

5.I4I3 

2.7641 

88.20 

O.  10 

0.5110 

5-IIOO 

2  .  7473 

87.36 

0.25 

I  .  3040 

5.2160 

2.8043 

0.50 

2.8371 

5^743 

3-0507 

0.75 

4.5860 

6.II47 

3-2874 

I.OO 

6.7157 

6.7157 

3-6105 

i-5 

12.1308 

8.0871 

4.3532 

2.0 

17.7342 

8.8671 

4-7672 

Table  XXXVI. — Conductivity  Measurements. 


/*oo  o°  =  117  (Jones  and  Bassett)1. 

F. 

Hv. 

a. 

IOO 

113.06 

96.63 

40 

104  .  86 

89.62 

20 

99.30 

84.80 

13-34 

96.00 

82.05 

IO 

92.26 

78.85 

4 

83.79 

7I.6l 

2 

73-86 

63.I4 

1-334 

66.15 

56.54 

i 

59-58 

50.92 

0.667 

48.59 

4L53 

0-5 

38.51 

32.91 

Table  XXXVII.—  Specific  Gravity 

Measurements  . 

m.            Sp.  gr. 

W50l.                      Wsalt. 

TTT                Per  cent  of 
w  Hzo-        correction. 

o.oi       1.001159 

IOOI.I59             L299 

999.860         0.014 

0.025     1.003052 

1003.052            3.247 

999.805         0.019 

o  .  05       i  .  006065 

IOO6.065            6.495 

999-5703      0.043 

0.075     1.009190 

1009.190            9-742' 

5     999-447       0.055 

o.io         .012386 

1012.386          12.990 

999  -  396       o  .  060 

0.25         .03049 

1030.491          32.475 

998.016       0.19 

0.50         .05492 

1054.924         64.95 

989.974       i.oo 

0.75         .09118 

1089.180         97.425 

991.655       0.83 

i.oo         .11847 

III8.47I       129.90 

988.571       1.14 

i-5           -17502 

1175.026       194.85 

980.176       1.98 

2.0              .23637 

1236.376         25.98 

976.576       2.34 

i  Am.  Chem.  J.,  33,  567  (1905). 


46 


m. 

0.025 
0.05 
0.075 

O.  10 

0.25 
0.50 
0.75 

I.OO 

1.5 

2.0 


a. 

89.62 
84.87 
82.05 
78.85 
71.61 
63.41 

56.54 
50.92 

41-53 
32.91 


Table  XXXVIII.—. 

L. 

5.1938 
5-0717 
4.9122 

4.7932 
4.7098 
4.2088 
3.9632 
3.7542 
3.4049 


3.0842 


5.5786 
5.2186 
5-I4I3 

5. i ioo 
5.2160 

5.6743 
6.1417 

6.7157 

8.0871 
8.8671 


-Hydrates. 

L'. 

M. 

5.5776 

3-822 

5.2164 

2.122 

5-1385 

2.444 

5  •  1070 

3.413 

5-2057 

5.292 

5.6176 

13-93 

5-9937 

18.22 

6.6394 

24.14 

7.9270 

3L69 

8.6594 

35-76 

H. 

152.88 
42.44 
33-68 

34-13 
28.31 
27.86 

25.09 
24.14 

21.  I 

17.88 


It  will  be  noted,  first  of  all,  that  the  freezing  point  lower- 
ings  for  all  concentrations  are  greater  than  for  any  of  the  salts 


AICI 


5T 


0.75      i 

Concen  tratlon . 
Fig.   V. 


47 


thus  far  studied,  and  hence  there  is  a  correspondingly  greater 
difference  between  the  observed  and  calculated  lowerings.  The 
amount  of  water  combined  with  the  salt  increases  regularly 
from  0.05  normal  to  the  most  concentrated  solution,  as  shown 
by  Fig.  VI.  The  hydration  per  molecule  decreases  rapidly 
in  the  most  dilute  solutions,  and  approaches  a  constant  value 
at  0.25  normal.  For  the  curve  for  hydrates,  see  Fig.  V. 


4-0 


fl.5 


0-75        1. 

Concentration. 
Fig.  VI. 


2.5 


Cobalt  Nitrate. 

Cobalt  nitrate,  like  cobalt  chloride,  crystallizes  with  6  mole- 
cules of  water,  and  we  should  expect  it  to  have  hydrating 
power  of  the  same  order  of  magnitude.  The  data  given  in 
the  following  tables  show  that  such  is  the  case.  What  has 
been  said  regarding  cobalt  chloride  applies  equally  well  to 
the  nitrate. 

The  curves  for  the  values  of  H  and  M  are  found  in  Figs. 
VII.  and  VIII.,  respectively. 


48 


6 


r 


z 


4.5 


Concentration . 
Fig.  VII. 


XXXIX. — Freezing  Point  Measurements. 


m. 

A. 

A/w. 

it 

a. 

O.IO 

0.0553 

5-5300 

2.9731 

98.65 

0.025 

O.I34I 

5-3640 

2.8731 

93.65 

0.05 

0.2572 

5.1434 

2.7652 

88.26 

0.075 

0.3812 

5.0826 

2.7218 

86.09 

O.IO 

0.5005 

5.0050 

2  .  7096 

85.48 

0.25 

I  .  2705 

5.0082 

2.7323 

0.50 

2.708 

5-4I7 

2.9125 

0.75 

4.338 

5.784 

3.1099 

I.OO 

6.22O 

6.22O 

3-3441 

1.5 

10.888 

7.192 

3.8668 

2.0 

18.863 

9-431 

5.0701 

49 


10 


Concentratl  on  . 
Fig.  VIII. 


Table   XL.—  Conductivity. 


V. 
ioo 

40 

20 

13-334 
10 
4 

2 

1-333 
i 

0.668 
0-5 


117.  6.  * 


108  .66 
100.69 
96.12 
91-67 
89  .94 
81.48 

72.94 

65.32 
58.89 
47.57 
37-io 


92  .  40 
85.62 
81.73 

77-95 
76  .  48 
69.28 

62.02 

55.54 
50.08 
40.45 
31-55 


J.    U/Ul'C-    J\.J-i±  . 

m.             Sp.  gr. 

wj^xt'^f'yux  \J 
WSOl, 

f  U/  V  flsj/     J.  VJ.  C-U/O  *»•/  C-  II  trf,  JM-0  . 

WsaU.          WH^O. 

Per  cent  of 
correction. 

0 

.OI          I.OOI496 

1001 

.496 

I 

•  830 

999 

.652 

0 

.033 

0 

.025       1.003863 

1003 

•863 

4 

•577 

999 

.286 

0 

.071 

0 

•05          1-007579 

1007 

•579 

9 

.154 

998 

•425 

0 

•157 

0 

.075       I.OII289 

ion 

.289 

13 

•731 

997 

.558 

0 

.244 

0 

.  IO 

.015084 

1015 

.084 

18 

.308 

996 

.776 

0 

.322 

0 

•25 

•03737 

1037 

.37 

45 

-77 

991 

.603 

0 

•83 

0 

•5 

.07415 

1074 

•15 

91 

•54 

982 

.61 

I 

•73 

0 

-75 

.  II204 

mo 

.04 

137 

.31 

972 

-73 

2 

.72 

i 

.00 

.  14612 

1146 

.  12 

183 

.08 

963.04 

3 

-69 

i 

.5 

.21720 

1217 

.20 

274 

.62 

942 

•58 

5-74 

2 

.0         1.28576 

1285 

-76 

366 

.16 

919.60 

8 

.04 

i 

Am.  Chem.  J.,  S3,  569 

(1905). 

50 
Table  XLIL— Hydrates. 


m. 

a. 

L. 

A/m. 

L'. 

M. 

ff. 

0. 

025 

85 

.62 

5- 

0451 

5-3640 

5 

.3602 

3 

.266 

130.6 

0. 

05 

81 

•73 

4- 

9003 

5-1434 

5 

•1354 

2 

-544 

50.8 

0. 

075 

77 

•95 

4- 

7597 

5.0826 

5 

.0702 

3 

.402 

45-3 

0. 

10 

76 

•48 

4- 

7050 

5-0050 

4 

.9889 

3 

.161 

31-6 

0. 

25 

69 

.28 

4- 

437 

5.082 

5 

.0296 

6 

•445 

25-8 

0. 

5 

62 

.02 

4- 

167 

5-4I7 

5 

.323 

12 

.070 

24.1 

0. 

75 

55 

•54 

3- 

926 

5.784 

5 

.627 

16 

.880 

22.5 

I. 

oo 

50 

.08 

3- 

723 

6.220 

5 

•990 

21 

.020 

21.  O 

I  . 

5 

40 

•45 

3- 

364 

7.192 

6 

.779 

27 

.980 

I8.7 

2.0    31.55  3-033   9-431   8.607   30.123   18.0 


Copper  Chloride. 

Diluted  portions  of  the  mother  solution  were  taken  and 
the  copper  in  them  determined  electrolytically. 

While  copper  chloride  crystallizes  with  two  molecules  of 
water,  its  power  to  combine  with  water  is  of  the  same  order 
of  magnitude  as  that  of  cobalt  chloride  and  cobalt  nitrate, 
as  may  be  seen  in  the  curves,  Figs.  V.  and  VII. 

The  total  amount  of  water  combined  with  the  electrolyte 
passes  through  a  minimum  at  about  0.05  normal  and  then 
increases  rapidly  with  increase  in  concentration.  This  is 
seen  in  Fig.  VI. 


Table  XL/77. — Freezing  Point  Measurements. 

a. 


m. 

A. 

A/w. 

(. 

O.OI 

O.OS7O1 

5  .  7OV) 

0.05 

"  •  v  \j  /  ^^O 

0.24944 

\}  i  ^"^O 

4.9888 

2.6821 

0.075 

0.37075 

4-9433 

2.6576 

O.IOO 

o  .  48665 

4-8665 

2.6164 

0.25 

1.2237 

4-894 

2.6316 

0.50 

2.669 

5-338 

2.8701 

0.75 

4-245 

5-66i 

3-0436 

I.OO 

5-994 

5-994 

3.2228 

1.50 

10.105 

6.737 

3.6220 

2.0 

15-294 

7.647 

4.  III2 

84. 10 

80.82 


Table  XLIV. — Conductivity  Measurements. 

/AOO  o°  =  1 20  (Jones  and  Bassett).1 

F.  /*».                                          a. 

loo  110.55  92.12 

20  95-88  79-98 

13.34  93.27  77.72 

10  90.21  75-17 

4  80.20  66.83 

2  6908  57.56 

1.334  61.03  50.86 

I  54.01  45.00 

0.6666  41.81  34.84 

0.5  31.56  26.30 


Table  XLV.  —  Specific  Gravity  Measurements. 


m. 

Sp.  gr. 

Wsol. 

Wsalt. 

Per  cent  of 
correction. 

O.OI 

.OOI208 

1001.208 

1-345 

999.863 

0.013 

0.05 

.006370 

1006.370 

6.725 

999-645 

0.035 

0.075 

.009264 

1009  .  264 

10.0875 

999.176 

0.084 

O.  IO 

.012614 

1012.614 

I3-450 

999.164 

0.263 

0.20 

.030991 

1030.991 

33-625 

997.366 

0.263 

0.50 

•051479 

1061.479 

67.25 

994.229 

0-57 

0-75 

.090912 

1090.91 

100.87 

990-037 

0-99 

I.OO 

.  120249 

1120.24 

134-5 

985  -  749 

1.42 

1.50 

.177618 

1177.61 

201.75 

975.868 

2.41 

2.0 

•234551 

1234.55 

269.0 

965.55 

3-44 

Table  XLV  I.  —Hydrates. 


m. 

a. 

L. 

b\m. 

L'. 

M. 

H. 

O. 

05 

79 

•98 

4 

8352 

4 

9888 

4.9871 

i 

•693 

33-85 

0. 

075 

77 

.72 

4 

4 

9433 

4.9392 

2 

.116 

28.21 

0. 

IO 

75 

•17 

4 

6563 

4 

8665 

4.8695 

2 

•354 

23-54 

0. 

20 

66 

-83 

4 

3460 

4 

8949 

4.8821 

6 

.091 

24-36 

0. 

50 

57 

.56 

4 

0012 

5. 

3384 

5  -  3076 

13 

.67 

27-34 

0. 

75 

50 

.86 

3 

7519 

& 

6611 

5-5748 

18 

-17 

24.22 

I  . 

oo 

45 

.00 

3 

5340 

5- 

9945 

5.9088 

22 

-33 

22.33 

I  . 

50 

34 

.84 

3 

1560 

6. 

7370 

6.5747 

26 

.66 

17.78 

2. 

00 

26 

•30 

2. 

8383 

7- 

6470 

7-3836 

34 

.20 

17.10 

I 

Am.  Chem. 

J.,35 

\,  576  (1905). 

52 

Copper  Nitrate. 

The  mother  solution  of  the  salt  was  diluted  to  convenient 
strength  and  the  copper  determined  electrolytically. 

Copper  nitrate  crystallizes  with  6  molecules  of  water  and, 
therefore,  should  give  us  hydration  of  the  same  order  of  mag- 
nitude as  that  found  for  the  nitrate  of  cobalt  and  nickel, 
which  crystallize  with  the  same  amount  of  water.  Refer- 
ence to  Table  L.  will  show  that  this  is  the  fact.  The  minimum 
for  the  total  amount  of  combined  water  is  pronounced  and 
lies  between  0.075  and  0.25  normal.  The  hydration  per  mole- 
cule decreases  rapidly  with  increase  in  concentration  to  0.25 
normal,  and  then  becomes  approximately  constant. 

The  curves  representing  the  values  of  H  and  M  are  given 
in  Figs.  VII.  and  VIII.,  respectively. 

Table  XLVII. — Freezing  Point  Measurements. 
m.  A.  Ajm.  i.  a. 


0.025 

0.13852 

o  •  /  ov«j 
5-5401 

o  -  •• 

2.9785 

98.92 

0.05 

0.25540 

5.I08I 

2.7463 

87.31 

0.075 

0.36979 

4.9306 

2.6508 

82.54 

0.25 

I.  221 

4.885 

2.6264 

81.32 

0.5 

2.589 

5.178 

2.7841 

0.75 

4.190 

5.587 

3.0039 

0-935 

5-512 

5.895 

3.1696 

1.50 

10.284 

6.856 

3.6861 

2.0  16.89  8.44  4-54I9 

Table  XLVIII. — Conductivity  Measurements. 
/*oo  o°  =  nS.1 

V.                                                  Mr.  a. 

loo                              108.84  92.24 

40                   IOI.2  85.76 

2O                    95.7  Sl.IO 

13-34                 91-86  77.85 

4                                  79.4  57.29 

69.8  

1-334                          62.0  52.54 

1.0695                        56.89  48.21 

0.667                         44-0  37-29 

0.5                              33-47  28.36 

Am.  Chem.  J.,  88,  578  (1905). 


53 
Table  XLIX. — Specific  Gravity  Measurements. 


m. 

Sp.  gr. 

Wsol. 

Wsalt. 

WHZO. 

Per  cent,  of 
correction 

O.OI 

1.001504 

iooi  .  5049 

1.876 

999.628 

0.037 

0.025 

I  .  004076 

1004  .  0764 

4.692 

999.384 

0.061 

0.05 

1.007859 

1007.8599 

9.384 

998.4759 

0.152 

0.075 

I.OII7I5 

IOII.7I55 

14.076 

997.6395 

0.236 

0.25 

I  .  040290 

1040.2903 

46  .  920 

993.370 

0.663 

0.50 

1.07723 

1077.230 

93.840 

983.390 

1.66 

0-75 

1  .  1  1469 

III4.699 

140.76 

973-930 

2.607 

0-935 

I.  14262 

1142.627 

174.48 

968  .  140 

3.188 

1-5 

I.226l8 

1226.  183 

281.52 

944  .  660 

5-53 

2.0 

I  .29262 

1292.623 

375.36 

917.26 

8.27 

Table  L.— -Hydrates. 


m. 

a 

L. 

A/w. 

L'. 

M. 

H, 

0.025 

75- 

76 

5 

.0502 

5-5401 

5 

.5368 

4- 

882 

195 

.2 

0.05 

81. 

10 

4 

.8769 

5.1081 

5 

.1005 

2. 

435 

48 

•  7 

0.075 

77- 

85 

4 

•756o 

4.9306 

4 

.9188 

I  . 

839 

24 

•5 

0.25 

67. 

29 

4 

•363 

4.885 

4 

•852 

5. 

607 

22 

•4 

0.50 

59. 

15 

4 

.060 

5.178 

5 

.092 

II. 

261 

22 

•5 

0-75 

52. 

54 

3 

.814 

5.587 

5 

.441 

16. 

612 

22 

•15 

0-935 

48. 

21 

3 

.653 

5.895 

5 

.708 

19- 

953 

21 

•3 

1.50 

37- 

29 

3 

.247 

6.856 

6 

•447 

27. 

575 

18 

.38 

2.0 

28. 

36 

2 

.914 

8.44 

7 

•749 

34- 

65 

17 

•32 

Nickel  Nitrate. 

The  nickel  was  determined  electrolytically  in  diluted  por- 
tions of  the  mother  solution. 

The  hydrating  power  of  nickel  nitrate  is  of  the  same  order 
of  magnitude  as  that  of  cobalt  and  copper  nitrates,  which  crys- 
tallize with  the  same  amounts  of  water  (see  Fig.  IX.).  The 
total  combined  water  passes  through  a  minimum  at  0.05  nor- 
mal and  then  increases  rapidly  with  increasing  concentra- 
tion (see  Fig.  X.). 


54 


Table  LI. — Freezing  Point  Measurements. 


m. 

A. 

A/w. 

i. 

a. 

O.OI 

0.0550 

5.5070 

2  .  9607 

98.03 

0.025 

0.1299 

5  -  1960 

2  .  7950 

89.75 

0.05 

0.2487 

4-9745 

2.6744 

83.72 

0.075 

o  .  3664 

4.8854 

2.6265 

81.32 

0.  10 

o  .  4960 

4.9602 

2.6667 

0.25 

1.251 

5-003 

2.69OI 

0.5 

2.652 

5-305 

2.8524 

0.75 

4-213 

5-6i8 

3.0205 

1.  00 

6.101 

6.  101 

3.2801 

1.5 

10.576 

7-051 

3.7910 

2.0 

17-050 

8.523 

4-5334 

Table  LII. — Conductivity  Measurements. 


117.  2 


V. 
100 

40 

20 
13.34 

10 
4 

2 


a. 


1-334 

i.o 

0.667 
0-5 


106.77 
100.31 

93.57 
89.74 

87.84 
80  .  07 

71-44 
64.06 

57.38 

45-79 
35.61 


91.10 
85.58 
79-83 
76.77 
74-94 
68.31 
60.95 
54-65 
48.95 
39-06 

30.38 


Table  LIII. — Specific  Gravity  Measurements. 


,,'JI 

w. 

Sp.  gr. 

w* 

oL 

Wsalt. 

Wi 

720. 

Per 
cor 

cent  c 
rectioi 

0 

.01 

.OOI52I 

IOOI 

•521 

i 

.8278 

999 

.693 

0 

.030 

0 

.025 

.003882 

1003 

.882 

4 

.5695 

999 

.312 

0 

.068 

0 

•05 

.007792 

1007 

.792 

9 

•139 

998 

•653 

0 

•134 

0 

.075 

.011541 

IOII 

•541 

13 

.7085 

997 

.029 

0 

.216 

0 

.10 

.015307 

1015 

•377 

18 

.278 

997 

.029 

0 

.291 

0 

.25 

.03837 

1038 

-37 

45 

•695 

992 

.68 

0 

.732 

0 

•5 

.07611 

1076 

.  ii 

9i 

•390 

984 

.72 

r 

.527 

0 

•75 

.11310 

1113 

.  10 

137 

.08 

976 

.01 

2 

•39 

I 

.0 

.  14562 

1145 

.62 

182 

•78 

962 

.88 

3 

.71 

I 

•  5 

.22134 

1221 

-34 

274 

•17 

947 

•17 

5 

.28 

2 

.0 

t  •  29459 

1294 

•59 

365 

.56 

929 

•03 

7 

.09 

*  Am.  Chem.  J.,  33,  574  (1905). 


55 

Table  LIV.— Hydrates, 
m.  a.  L.  A/m.  L' .  M.          H. 


0.05 

79 

•83 

4 

.8296 

4- 

9745 

4 

.9679 

i. 

545 

30.9 

0.075 

76 

.0 

4 

.7084 

4- 

8854 

4 

•8749 

i. 

797 

25-3 

0.075 

76 

•57 

4 

.7084 

4- 

8854 

4 

.8749 

i  . 

897 

25-3 

O.  10 

74 

•94 

A 

.6477 

4- 

9675 

4 

.8721 

2. 

560 

25.6 

0.25 

68 

•3i 

4 

.401 

5- 

0036 

4 

.9670 

6. 

329 

25-3 

0.50 

60 

•95 

4 

.127 

5- 

305 

5 

.225 

ii  . 

672 

23-3 

0.75 

54 

•65 

3 

.894 

5- 

618 

5 

.484 

16. 

IO2 

21.4 

I.OO 

48 

•95 

3 

.700 

6. 

102 

5 

•875 

20. 

561 

20.5 

1.5 

39 

.06 

3 

•313 

7- 

051 

6 

.679 

27. 

998 

18.6 

2.O 

30 

•38 

2 

•990 

8. 

525 

7 

.921 

34- 

58 

17-3 

Before  going  farther,  it  will  be  interesting  to  note  the  great 
similarity  between  the  salts  of  cobalt,  copper,  and  nickel  which 
we  have  just  studied.  Solutions  of  the  same  concentrations 
were  used  in  all  five  salts. 

Reference  to  Figs.  VI.,  VIII.,  and  X.  will  show  at  a  glance 
the  close  relation  between  the  amounts  of  water  held  in  com- 
bination by  these  salts,  whether  they  are  chlorides  or  nitrates. 
We  are  not  surprised  at  this,  since,  with  the  exception  of  cop- 
per chloride,  all  crystallize  with  6  molecules  of  water.  In 
fact,  we  found  it  impossible  to  put  more  than  two  curves  on 
one  sheet,  so  closely  did  the  values  agree.  From  the  min- 
imum in  the  most  concentrated  solutions  studied,  the  magni- 
tude of  the  hydrating  power  is  a  linear  function  of  the  concen- 
tration. In  other  words,  each  hydrate  has  its  own  definite 
composition,  which  varies  with  every  concentration. 

The  curves  representing  the  hydration  per  molecule  (Figs. 
V.,  VII.,  and  IX.)  show  the  same  striking  similarity.  They  are 
almost  asymptotic  with  the  two  coordinates.  The  hydration 
per  molecule  decreases  very  rapidly,  for  the  very  dilute  solu- 
tions, to  approximately  the  same  concentration,  when  they 
become  nearly  constant  for  further  increase  in  concentration. 

Two  conclusions  are  to  be  drawn  from  these  relations.  It 
will  be  noted  that  the  molecular  hydration  and  the  total  amount 
of  water  held  in  combination  are  the  same  for  any  two  salts 
containing  a  common  cation.  It  seems  most  probable  that 

if  the  two  anions,  Cl  and  NO3,  possess  very  different  hydra- 


0.1     0..25       0-5 


Concentration. 
Fig.  IX. 

ting  power,  this  influence  would  manifest  itself.  It  is  a  well- 
known  fact  that  organic  acids  possess  little  or  no  hydrating 
power,  and  in  the  work  which  I  have  done  upon  the  strong 
acids — hydrochloric,  nitric,  and  sulphuric — this  has  been  found 
to  hold  in  the  dilute  solutions,  where  the  dissociation  is  prac- 
tically complete. 

This  would  lead  us  to  conclude  that  the  hydrating  power 
of  any  salt  is  primarily  a  function  of  the  cation. 

In  the  discussion  of  the  nitrates  and  chlorides  of  the  alkaline 
earth  group,  attention  was  called  to  the  fact  that  the  hydra- 
ting  power  of  those  salts  is  an  inverse  function  of  the  atomic 
volumes. 


57 

In  the  case  of  the  salts  of  cobalt,  copper,  and  nickel  which 
we  have  studied,  we  have  to  do  with  cations  which  have  ap- 
proximately the  same  atomic  volumes. 

As  stated  by  Ostwald,1  the  migration  velocity  of  an  organic 
acid  decreases  with  increase  in  the  mass  of  the  anion,  as  well 
as  with  increase  in  the  mass  of  the  cation  in  case  of  the  organic 
bases.  We  should  expect,  then,  to  obtain  larger  values  for 
conductivity  than  those  given  by  the  alkaline  earth  metals. 
Experiment  shows  the  opposite  to  be  the  fact.  We  are,  there- 
fore, forced  to  believe  that  the  effect  of  the  atomic  volume 
of  the  ions  upon  the  conductivity  is  more  than  compensated 
for  by  the  relatively  large  volume  of  the  ionic  complex. 

Bredig2  pointed  out  the  fact  that  the  migration  velocities 
of  elementary  cations  are  a  periodic  function  of  the  atomic 
weights.  When  plotted  in  a  curve,  where  the  ordinates  rep- 
resent velocities  and  the  abscissas  the  atomic  weights,  it  will 
be  seen  that  the  alkali  metals  lie  very  near  the  maxima  of 
the  curve,  along  with  the  halogens.  At  the  extreme  minima 
we  find  aluminium  and  chromium.  Slightly  above  these  lie 
the  metals  of  the  copper  group,  zinc,  and  cadmium;  while 
still  higher  are  to  be  found  the  metals  of  the  alkaline  earths. 

The  significance  of  this  periodic  relation  between  the  migra- 
tion velocities  of  the  cations  and  the  atomic  weights  has  never 
been  satisfactorily  explained. 

We  believe  that  we  have  found  the  cause  of  this  phenomenon. 
Of  two  ions  or  ionic  complexes  of  different  volumes,  that  one 
will  meet  with  less  friction  on  moving  through  the  solution 
which  has  the  smaller  volume.  Consequently,  it  will  have 
the  greater  velocity.  On  the  other  hand,  the  greater  the  vol- 
ume, the  greater  will  be  the  friction  to  be  overcome  by  the 
ion,  and,  hence,  the  smaller  the  velocity.  Therefore,  we  should 
expect  to  find  that  those  salts  which  crystallize  with  little 
or  no  water  of  crystallization  give  greater  values  for  conduc- 
tivity than  those  crystallizing  with  a  greater  amount. 

It  is  a  well-known  law  that  the  conductivity  of  an  electro- 
lyte depends  upon  the  velocities  of  the  ions.  These  veloci- 
ties, in  turn,  depend  upon  the  fluidity  and  the  volume  of  the 

1  Lehrbuch,  2,  679. 

»  Z.  physik.  Chem.,  13,  242  (1894). 


58 

ion.     The  greater  the  volume,  the  greater  will  be  the  resist- 
ance offered  to  the  movement  of  the  ions. 

If  we  consider  the  alkalis  we  find  that  potassium,  rubidium, 
and  caesium,  which  have  the  largest  atomic  volumes  and 
whose  salts  generally  crystallize  without  water,  have  the  great- 
est migration  velocities,  while  lithium  and  sodium,  which  have 
smaller  atomic  volumes  and  whose  salts  crystallize  with  two 
or  three  molecules  of  water,  have  very  much  smaller  migra- 
tion velocities. 

Comparing  the  members  of  the  calcium  group,  we  find  that 
the  atomic  volumes  increase  with  increasing  atomic  weight. 
The  migration  velocities  of  the  cations  calcium  and  strontium, 
whose  salts  usually  crystallize  with  6  molecules  of  water,  are 
approximately  equal  to  that  of  the  barium  cation,  whose 
salts  crystallize  either  with  two  molecules  of  water,  or  water- 
free.  On  the  other  hand,  the  magnesium  cation,  of  smaller 
atomic  volume,  has  a  slightly  smaller  migration  velocity,  due 
to  the  more  complex  composition  of  its  hydrates. 

The  cations  of  cobalt,  copper,  and  nickel  have  approximately 
'the  same  atomic  weights,  the  same  atomic  volume,  and  the  same 
hydrating  power.  Since  these  cations  have  the  greatest 
hydrating  power  of  any  which  we  have  studied,  we  should 
expect  them  to  have  the  smallest  migration  velocities,  and 
such  is  the  case. 

Aluminium  Chloride. 

Special  interest  is  attached  to  the  study  of  aluminium 
chloride,  owing  to  the  fact  that  it  is  a  quaternary  electrolyte 
and  crystallizes  with  six  molecules  of  water. 

The  hydrolytic  effect  of  water  upon  this  salt,  in  dilute  solu- 
tions, can  be  noted  in  the  first  two  concentrations.  The  hy- 
drochloric acid  liberated  is  almost  completely  dissociated 
at  the  dilutions  in  question,  thus  giving  values  for  L  which  are 
considerably  higher  than  would  be  obtained  if  the  salt  were 
not  hydrolyzed.  This  may  be  attributed  to  one  of  two  causes : 
the  very  high  migration  velocity  of  the  hydrogen  ion;  its  ina- 
bility to  form  hydrates;  or  both.  It  is  at  about  0.075 
normal  that  the  influence  due  to  the  hydration  of  the  alumin- 
ium cation  begins  to  predominate.  Just  as  we  should  ex- 


59 

pect,  the  number  of  molecules  of  water  held  in  combination 
by  one  molecule  of  the  electrolyte  is  large  and  increases  very 
rapidly  with  increase  in  concentration  (see  Fig.  VI.).  In  the 
curve  representing  the  hydration  per  molecule  (Fig.  V.), 
that  part  representing  concentrations  between  0.075  and  0.5 
normal  represents  the  abnormality  in  the  hydration  due  to 
hydrolysis. 

A  glance  at  column  a  (Table  LVIII.)  shows  us  that,  in  spite 
of  the  tendency  of  this  salt  to  hydrolyze,  the  dissociation  de- 
creases very  rapidly  with  increase  in  concentration.  This 
is  just  what  might  be  predicted.  Its  atomic  volume  is  very 
small  and  the  hydrating  power  of  its  cation  very  large.  There- 
fore, it  should  have  a  very  small  migration  velocity. 

Table  LV. — Freezing  Point  Measurements, 
m.  A.  A/*».  i.  a. 

o.oi  0.712  7.1200  3.8279         94.26 

0.025  0.1623  6.4940  3.4193         80.64 

0.05  0.3053  6.1060  3.2827          76.09 

0.075  0.4511  6.0153  3.2340         74-46 

o.io  0.4511  6.0850  3.2704 

0.25  1.6604  6.641  3.5708 

0.50  3-9446  7.889  4-2415 

0-75  7-1339  9-5H  5-H37 

i.  oo  n.795  n-795  6.341 

1.5  25. 51  17.000  9-I398 

2.0  48. 51  24.25  13-037 

Table  LVI. — Conductivity  Measurements. 

Poo  o°  =  i7o.2 

V.                fj.v.  a. 

100            156.48  92.04 

40            141.24  83.08 

20  130.44  76.72 

13.334  126.66  74-50 

10  122.07  71.80 

4  106 .90  62 . 88 

2  88.60  52.11 

1-333  75-02  44.12 

i  61.93  36.42 

1.6667  41.62  24.48 

0.5  25.47  14.98 

1  These  freezing  points  were  determined  by  means  of  an  alcohol  thermometer 
and  freezing  mixtures  of  solid  carbon  dioxide  and  ether. 
*  Am.  Chem.  J.,  31,  333  (1904). 


6o 


Table  LVH.  —  Specific 

Sp.gr.  Wsol. 


Gravity  Measurements. 

Wsalt. 


Per  cent  of 
correction. 


0 

.OI 

.00104 

IOOI 

.04 

i 

•3345 

999 

•7i 

0 

.029 

0 

•025 

.00282 

IOO2 

.82 

3 

•3625 

999 

•49 

0 

•  051 

0 

•05 

.00588 

1005 

.88 

6 

.6725 

999 

.21 

0 

.079 

0 

•075 

.00870 

1008 

.70 

10 

.0087 

998 

.70 

0 

.130 

0 

.  I 

.01158 

IOII 

.58 

13 

•345 

998 

.24 

0 

.176 

0 

•25 

.02911 

1029 

.  ii 

33 

•36 

995 

•75 

0 

•425 

0 

•55 

.05706 

1057 

.06 

66 

•725 

990 

•33 

0 

.966 

.08431 

1084 

•31 

IOO 

.087 

988 

.22 

I 

•57 

I 

.00 

.11054 

1  1  10 

•54 

133 

•45 

977 

.09 

2 

.29 

I 

•5 

.  16308 

1163.08 

200 

•175 

962 

•905 

3 

.70 

2 

.00   1.21378 

1213 

.78 

266 

.90 

946 

.88 

5 

•3i 

Table  LV  III. —Hydrates. 


1 

o 

m. 
.01 

1 

Q2 

a. 
.04 

L. 
6.9958 

7 

A/w. 
.  I2OO 

7 

L'. 

.1180 

M. 

H. 

o 

.025 

-7 

8^ 

T^ 

.08 

J7Z7  \j 

6.4QS8 

6 

.4Q4O 

6 

.4007 

o 

•  \^**  ^j 

.OS 

O 

76 

.  72 

*T;7»_/ 

6.  I4OQ 

6 

i  ^7^^^ 

.  1060 

6 

T^  X   / 

.  IOI2 

o 

•  **vP 

.075 

/ 

74 

/ 

.  so 

V     A  .i-f-V^^ 

6.0111 

6 

•  1526 

6 

•  1447 

0 
0 
0 

I 

2 

^*  /  \J 

.  IO 

•  25 

•  5 
.00 

.0 

/  T^ 

71 
62 

44 
36 
24 
14 

*-J 

.80 
.88 

.  12 

•42 
.48 
.98 

5.8664 

5-368 

4.321 
3.892 
3-225 
2.695 

6 
6 

ii 
17 
24 

.1560 
.641 

-795 
.000 

-25 

6 
6 

9 
ii 
16 

22 

fcj-fef.  ^ 

.1452 
.613 
.362 
•523 
•369 
•963 

2 
10 

9 

36 

44 
49 

•52 
•54 
•9i 
.78 
.60 
•03 

25.2 
42.16 
39.88 
36.78 
29-33 
24-5I 

Sodium  Bromide. 

Dilute  portions  of  the  mother  solution  were  standardized 
volumetrically  by  Volhard's  method,  This  salt  differs  from 
those  preceding  in  that  it  is  a  binary  electrolyte  and  crystal- 
lizes with  two  molecules  of  water.  A  study  of  Table  LXII. 
brings  out  the  same  general  results.  The  observed  molecular 
lowering  passes  through  a  minimum  between  0.5  and  0.75 
normal.  The  minimum  in  the  total  amount  of  combined 
water  occurs  at  o.io  normal.  From  the  amounts  of  water 
which  combine  with  one  gram  molecule  of  the  salt,  it  will  be 
seen  that  the  sodium  cation  has  nearly  the  same  hydrating 
power  in  dilute  solutions  as  do  the  cations  of  the  calcium  and 
copper  groups. 

The  atomic  volume  of  sodium  is  slightly  more  than  half 


6i 

that  of  potassium.  Its  hydrating  power,  however,  for  the 
more  dilute  solutions  is  much  greater.  If,  then,  the  amount 
of  hydration  of  the  sodium  ion  is  more  than  sufficient  to  com- 
pensate for  the  inverse  volume  relations,  we  should  expect  the 
migration  velocity  of  sodium  to  be  less  than  that  of  potassium. 
This  has  been  found  to  be  the  case.1 

The  atomic  volume  of  sodium  is  also  slightly  less  than  that 
of  calcium,  and  considerably  less  than  those  of  strontium  and 
barium;  yet,  owing  to  the  greater  hydration  of  the  cations 
of  the  calcium  group,  its  migration  velocity  is  greater. 

For  the  curves  representing  the  values  of  H  and  M,  see  Figs. 
IX.  and  X. 

Table  LIX. — Freezing  Point  Measurements, 
m.  A.  A/w.  i.  a. 


0.025 

0.0952 

3  .  8090         i 

i  .  0478 

104.78 

0.05 

0.1863 

3.7260         ; 

2  .  0032 

100.32 

0.075 

0.2727 

3-636 

.9548 

95.48 

O.  IO 

0.3572 

3-572 

.9204 

92.04 

0.25 

0.885 

3-543 

.9049 

90.49 

0.50 

1.787 

3-574 

.9215 

0.75 

2.696 

3-595 

.9327 

I.  00 

3-633 

3.633 

.9481 

1.5 

5-654 

3.769           < 

2.0263 

2.OO  7.746  3-873  2.O822 

Table  LX. — Conductivity  Measurements. 

/*oo  o°  =  64. 48.2 
V.  to.  «. 

94-78 

9L53 
89.44 

87.36 

85.73 
79.21 

76.78 
76.08 

73.83 
70.56 

66.22 


IOO 

6l  .  12 

40 

59-02 

20 

57.67 

13-334 

56.33 

10 

55.28 

4 

51.08 

2 

49-51 

1-333 

49.06 

I 

47.61 

0.6667 

45-50 

0-5 

42.70 

1  Bredig:  Z.  physik.  Chem.,  13, 

242  (1894). 

»  Am.  Chem.  J.,  34,  375  (1905). 

62 


o.oi 
0.025 
0.05 
0.075 

O.IO 

0.25 

0.50 

0.75 

1. 00 

i-5 

2.OO 


4-0 


30 


20 


O-75          1. 

Concentration. 
Fig.  X. 


1.5 


Table  LXI. — Specific  Gravity  Measurements. 
Sp.gr.  Wsoi.  WSait. 


Per  cent  of 
correction. 


.000732 
.002177 
.  004074 
.005972 
.00788 
.01964 
.03908 
.05811 
.07632 
.11963 
.15240 

IOOO 
1002 
1004 
1005 
IOO7 
1019 
1039 
1058 
1076 
III9 
1152 

•732 
.177 
.074 
•972 

.88 
.64 
.08 
.  ii 
•32 
•63 
.40 

i. 

2. 
5- 
7- 
10. 

25- 

77- 
103. 

154- 
206. 

030 

575 
150 
725 
30 
75 
50 
25 

01 
02 

999 
999 
998 
998 
997 
993 
987 
980, 

973 
965 
946. 

70 
602 
924 

247 
58 
89 
58 
86 

12 

38 

O. 
O. 
0. 

o. 

0. 

o. 
I. 
I. 

2. 

3- 

5- 

030 
040 

107 
175 
24 

61 
24 

66 
48 
36 

Table  LXIL— Hydrates. 


nt. 

a. 

L. 

A/w. 

Z'. 

M. 

H. 

0.025 

91 

•53 

3 

.5624 

3 

.805 

3- 

8075 

3- 

575 

143-0 

0.05 

89 

•44 

3 

.5235 

3 

.7260 

3- 

7221 

2. 

963 

59-2 

0.075 

87 

.36 

3 

.4848 

3 

•636 

3- 

6297 

2. 

217 

24.29 

O.IO 

85 

•73 

3 

•4545 

3 

•572 

3- 

5635 

I  . 

700 

17.00 

0.25 

79 

.21 

3 

•333 

3 

•543 

3- 

521 

2. 

974 

11.89 

0.50 

76 

.78 

3 

.288 

3 

•574 

3- 

529 

3- 

803 

7.60 

0.75 

76 

.08 

3 

•275 

3 

•595 

3- 

526 

3- 

961 

5-28 

1.  00 

72 

.83 

3 

•233 

3 

•633 

3- 

536 

4- 

763 

4.76 

1.5 

70 

-56 

3 

.172 

3 

•769 

3- 

637 

7- 

103 

4-73 

2.OO 

66 

.22 

3 

.  IOI 

3 

•873 

3- 

665 

8. 

547 

4-27 

63 
Hydrochloric  Acid. 

Having  investigated  fifteen  salts,  I  next  turned  my  at- 
tention to  the  study  of  some  of  the  more  common  acids. 

An  approximately  three  normal  solution  of  hydrochloric 
acid  was  prepared.  Dilute  portions  of  the  mother  solution 
were  then  titrated  against  a  standard  solution  of  potassium 
hydroxide  free  from  carbonate.  This,  in  turn,  had  been  stand- 
ardized by  means  of  a  tenth  normal  solution  of  freshly  pre- 
pared oxalic  acid.  The  results  are  given  in  Tables  LXIII. 
to  LXVI. 

A  glance  at  Table  LXVI.  shows  that,  for  the  more  dilute 
solutions,  the  corrected  observed  freezing  point  lowering  (Lf) 
is  less  than  that  calculated  from  the  dissociation.  This  is 
due  to  one  of  two  causes:  the  very  high  migration  velocity 
of  the  hydrogen  ion,  or  its  inability  to  form  hydrates. 

The  minimum  in  the  freezing  point  lowering  occurs  at  about 
0.25  normal.  For  dilutions  greater  than  0.5  normal,  there 
is  no  evidence  of  hydration.  At  0.5  normal,  however,  the 
hygroscopic  property  of  the  molecular  hydrochloric  acid  be- 
gins to  predominate  over  the  effect  of  decrease  in  dissociation. 
From  this  point  the  amount  of  combined  water  increases 
with  increase  in  concentration.  The  corresponding  values 
of  H  differ  from  those  of  the  other  electrolytes  thus  far  studied 
in  that  they,  also,  increase  as  the  concentration  increases. 

The  values  of  H  and  M,  for  hydrochloric  acid,  are  plotted 
in  Figs.  I.  and  II. 

Table  LXIII. — Freezing  Point  Measurements, 
m.  A.  A/w.  /.  a. 


0.025 

o  .  0902 

3.6080 

•9377 

93-97 

0.05 

0.1799 

3  •  598o 

-9344 

93-44 

0.075 

0.2681 

3-5752 

.9221 

92.21 

0.  IO 

0.3567 

3-5670 

.9177 

91.77 

0.25 

0.8862 

3-5450 

-9059 

90.59 

0.50 

I.84I 

3.682     ] 

•9794 

0.75 

2.852 

3.804    : 

2.0450 

1.  00 

3-975 

3-975    2 

1.1372 

1.50 

6.452 

4-301      2 

J-3I23 

2.0O 

9.367 

4-683    2 

'•5177 

64 


Table  LXIV.  —  Conductivity  Measurements. 

/^oo   0°   =   236.92. 

y. 

A*z>. 

a. 

40 

233.95 

98.75 

20 

232.60 

98.18 

13-33 

231.87 

97.87 

10 

228.61 

96.49 

4 

222.  17 

93-77 

2 

211.79 

89.39 

1-333 

203.28 

85.80 

i 

199.85 

84.35 

0.667 

l8l.79 

76.73 

0.5 

I68.O4 

70.93 

Table  LXV. — Specific  Gravity  Measurements. 


m. 
0.025 

Sp.  gr. 
[.00034 

1000.34 

W5alt. 
O.9II 

999.429 

Per  cent  of 
correction. 

0.057 

0.05 

[.OOIOI 

IOOI.OI 

1.822 

999.188 

O.oSl 

0.075 

.00135 

1001.35 

2.734 

998.616 

0.138 

O.IO 

.00180 

1001.80 

3-645 

998.155 

o.  184 

0.25 

.00425 

1004.25 

9.II4 

999.136 

0.486 

0.50 

.00849 

1008.49 

18.229 

99O.26I 

0-973 

0.75 

.01264 

1012.64 

27-343 

985.297 

i-47 

I.OO 

.01749 

1017.49 

36.458 

981.032 

1.896 

1.5 

.02542 

1025.42 

54-687 

970-733 

2.92 

2.O 

•03414 

1034.14 

72.916 

961.224 

3.87 

Table  LXV  I.  —Hydrates. 


m. 
0.025 
0.05 
0.075 
O.IO 

0.25 
o.  20 

a. 

98.75 
98.18 

97-87 
96.40 

93-77 

L. 

3.6967 
3.6861 
3.6803 

3-6547 
3-604I 

1   CQ2I 

3.6080 
3-598o 
3-5752 
3-5670 

T.  C'Jio 

L'. 
3.6060 

3-5702 
3-56IO 
3.5280 
36260 

0.75 

I.OO 

1.5 

2.0 

85.80 
84.35 
76.73 
70.93 

O  •  Ov/<*  J 

3-455 
3.428 
3.287 
3-179 

O  -  OOAV^ 

3.803 

3-975 
4-301 
4-683 

*  v/Av^vy 

3-747 
3.899 
4.176 
4.502 

M. 


H. 


1.580  3.16 

3-33  5-77 

6.707  6.70 

11.820  7.88 


65 

Nitric  Acid. 

A  moderately  concentrated  solution  was  first  made  up, 
care  having  been  taken  that  the  acid  used  contained  none 
of  the  oxides  of  nitrogen  in  solution. 

Dilute  portions  of  this  were  standardized  volumetrically 
against  a  solution  of  potassium  hydroxide. 

Like  hydrochloric  acid,  dilute  solutions  of  nitric  acid  ex- 
hibit no  tendency  to  form  hydrates.  No  appreciable  power 
to  combine  with  water  is  manifested  until  the  concentration 
0.75  normal  is  reached.  The  amount  of  total  combined  water, 
then,  increases  with  increase  in  concentration.  The  same  re- 
sults are  obtained  for  the  values  of  H.  For  curves  repre- 
senting the  values  of  H  and  M  see  Figs.  III.  and  IV. 

Table  LXVII. — Freezing  Point  Measurements. 


m. 

A. 

A/w. 

t. 

a. 

0.025 

0.09035 

3.6140           3 

•9430 

94-30 

0.05 

O.I79I 

3.5830          '1 

•9263 

92.63 

0.075 

0.2678 

3-5713         "1 

.9200 

92.00 

O.  IO 

0-3547 

3  •  5470         l 

.9069 

90.69 

0.25 

0.8869 

3-4576       ,J 

•9073 

90.73 

0.50 

1.798 

3-597        ,.J 

•9341 

0.75 

2.766 

3.681 

•9736 

I.OO 

3-749 

3-749           i 

2.0156 

i-5 

5-955 

3-970          : 

2.1344 

2.O 

8-383 

4.191           : 

2.2532 

Table  LXVIII. — Conductivity  Measurements. 

^oo  o°  =  237.07. 

V.                                         itv.  a. 

40                                     234.89  99.08 

20                                                  233.88  98.65 

13-33                  229.66  96.87 

10              226.24  95-43 

4              222.82  93-99 

2              216.63  9I-38 

1.334          211.43  89.17 

i.o            203.72  85.93 

0.5            177.15  74.71 


66 


Table  LXIX. — Specific  Gravity  Measurements. 


m.     Sp.  gr. 

Wsol. 

Wsalt.    WH&. 

Per  cent  of 
correction. 

O. 

025  1.000926 

1000 

.926 

I. 

576 

999 

•35 

O 

.065 

0. 

05   1.001798 

IOOI 

.798 

3- 

152 

998 

.64 

0 

•134 

0. 

075 

.002653 

IOO2 

.653 

4- 

728 

997 

-92 

0 

.207 

O. 

10 

.003496 

1003 

.496 

6. 

304 

997 

•  J9 

0 

.281 

0. 

25 

.008481 

I008 

.48 

15- 

762 

992 

.71 

0 

.728 

0. 

5 

.01686 

1016 

.86 

3i. 

524 

985 

•34 

I 

•465 

0. 

75 

.02503 

1025 

•03 

48. 

280 

976 

-75 

2 

-325 

I  . 

oo 

.03360 

1033 

.60 

63- 

050 

970 

•55 

2 

-945 

2. 

00 

.06700 

1067 

.00 

126. 

090 

940 

•91 

5 

.909 

Table  LXX.— Hydrates. 


nt. 

0.025 
0.05 
0.075 
O.  IO 

0.25 

0.5 

0.75 

I.OO 
2.OO 


a. 

99.08 
98.65 
96.87 

95-43 
93-99 
91-38 
89.17 
85.93 
74-71 


L. 
3.7028 


A/w. 
3.6140 


L'. 

3.6124 
3-5790 
3-5640 
3-5370 
3-5210 
3-544 
3-595 
3-639 
3-944 


M. 


H. 


3.6948  3.5830 

3.6617  3-57I3 

3.6348  3.5470 

3.6062  3.5476 

3-559  3-597  

3.518  3.680  3.595  1.180  1.57 

3.450  3.749  3-639  2.880  2.88 

3.249  4.191  3.944  9.78  4.89 

Sulphuric  Acid. 

Dilute  portions  of  the  mother  solution  were  titrated  against 
the  standard  potassium  hydroxide  used  for  the  previous  acids. 

The  results  are  given  in  Tables  LXXI.  to  LXXIV. ;  the  curves 
in  Figs.  IX.  and  X. 

In  dilute  solutions  no  water  is  held  in  combination.  The 
total  amount  of  water  held  in  combination  by  the  acid,  and 
the  hydration  per  molecule,  increases  with  concentration  from 
0.75  to  2  normal. 

Table  LXXI. — Freezing  Point  Measurements. 


m. 

A. 

A/*v. 

i. 

a. 

O.OI 

0.04872 

4.8720 

2.6193 

80.96 

0.025 

0.1179 

4.7184 

2.5367 

76.84 

0.050 

0.2182 

4.3640 

2  •  3462 

67.31 

0.075 

0.3157 

4.2099 

2  •  2634 

63.17 

O.  IO 

0.4043 

4-0434 

2.1738 

58.69 

0.25 

0.9865 

3-946o 

2.I2I5 

56.07 

0.50 

2.0033 

4.0066 

2.I54I 

o.75 

3-H74 

4-I56 

2.2346 

I.OO 

4-379 

4-379 

2  -  3544 

1.50 

7.265 

4.843 

2.6042 

2.0 

11.296 

5.648 

3-0365 

67 


Table  LXXII. — Conductivity  Measurements. 


V. 

100 

40 

20 

13-34 
IO 

4 

2 

1-334 

I.OO 

0.6667 
0.5 


0°   =  485-42- 

(*v. 

398.34 
353-41 
335.56 
323.43 
314.42 
296:30 
281.52 
271.25 
259.05 
234.38 

209 . 28 


a. 

82.06 
72.80 

69-13 
66.63 
64.78 
61.04 

57-99 

55-88 

53-37 
48.28 

43-n 


Table  LXXIII.—  Specific 
m.            Sp.  gr.             Wsoi. 

Gravity  Measurements. 

W    n           U/tr  r*        Per  cent  °f 
Wsalt.         WH&.      correction. 

O.OI 

.000719 

IOOO 

.719 

O. 

980 

999- 

74 

0 

.026 

O. 

025 

.001907 

1001 

•9i 

2. 

45i 

999- 

45 

0 

•054 

0. 

05 

•003551 

1003 

•55 

4- 

902 

998. 

65 

0 

•135 

0. 

075 

•005152 

1005 

•15 

7- 

353 

997- 

79 

0 

.220 

0. 

I 

.00677 

1006 

•77 

9- 

807 

996. 

97 

0 

•303 

o. 

25 

.01618 

1016 

.18 

24- 

51 

991. 

67 

0 

•  832 

0. 

5 

.03218 

1032 

.18 

49- 

03 

983- 

H 

I 

.68 

0. 

75 

.04760 

1047 

.60 

73- 

53 

974- 

07 

2 

•59 

I  . 

00 

.06307 

1063 

•07 

98. 

07 

964. 

99 

3 

•50 

I  . 

5 

•09345 

1093 

•45 

147. 

ii 

946. 

34 

5 

-36 

2. 

o 

.12316 

1123 

•51 

196. 

15 

926. 

99 

7 

•30 

Table  LXXIV.— Hydrates. 


0 
0 
0 

o 

0 
0 
0 
0 

I 
I 

2 

m. 

.01 

.025 
•05 
.075 

.  IO 

.25 

-5 

•75 

.0 

•5 

.0 

a 
82. 
72. 
69. 
66. 

61. 

57- 
55- 
53- 
48. 
43- 

06 
80 

04 
99 

88 

37 
28 
ii 

4- 
4- 
4- 
4- 
4- 
4- 

3- 
3- 
3- 
3. 

L. 
9126 
5681 
43i6 
3386 
2698 

017 
938 
845 
656 
464 

4 
4 
4 
4 
4 
3 
4 
4 
4 
4 
5 

A/w. 
.8720 
.7184 
.3640 
.2099 

•0434 
.9460 
.266 
.156 
•379 
•844 
.6481 

4 
4 
4 
4 
4 
3 
3 
4 
4 
4 
5 

.8708 

.2007 
.0312 
.9132 

•939 
.048 
.226 

-585 
•  236 

M. 


H. 


I.5I2  2.00 

5.004  5.00 

11.257  7-50 

18.801  9.40 


1  Jones  and  Getman:  Z.  physik.  Chem.,  46,  272  (1903). 


68 

A  comparison  of  Figs.  L,  III.,  and  IX.  shows  that  the  hy- 
drating  powers  of  hydrochloric  and  sulphuric  acids  are  of  ap- 
proximately the  same  order  of  magnitude,  while  that  of  nitric 
acid  is  slightly  less. 

Figs.  II.,  IV.,  and  X.,  representing  the  total  amounts  of 
combined  water  for  the  three  acids,  show  that  the  same  re- 
lation holds  here  as  for  the  hydrates. 

Discussion. 

Fifteen  salts  and  three  strong  acids  have  been  studied  in 
this  investigation.  I  have  worked  with  solutions  cover- 
ing a  range  of  concentration  from  o.oi  to  2.0  normal ;  at  one 
extremity  are  found  to  predominate,  in  a  very  pronounced 
manner,  those  influences  due  to  the  ions;  at  the  other,  those 
due  to  the  molecules  also  manifest  themselves.  In  this  way 
I  have  attempted  to  compare  the  relative  effects  of  the  ions 
and  the  molecules  upon  the  molecular  lowering  of  the  freezing 
point  and  the  dissociation. 

Comparing,  first  of  all,  the  freezing  point  lowerings  for  any 
given  solution,  it  is  found  that,  without  exception,  the  molec- 
ular lowering  calculated  from  the  dissociation  decreases  regu- 
larly with  increasing  concentration.  Naturally,  this  follows 
from  the  fact  that  the  decrease  in  dissociation  is  regular 
throughout.  On  the  other  hand,  the  corrected  observed 
freezing  point  lowering  decreases  very  rapidly  in  the  dilute 
solutions,  passes  through  a  very  pronounced  minimum,  and 
then  increases  as  the  concentration  increases.  A  glance  at 
the  tables  of  the  hydrates  shows  that  in  every  case  the  ob- 
served molecular  lowering  produced  by  any  salt  is  greater 
than  the  calculated  lowering  based  on  conductivity  measure- 
ments. 

If  there  were  no  hydration,  we  should  expect  the  observed 
and  the  calculated  molecular  lowerings  to  be  equal,  except 
for  the  difference  due  to  the  influence  of  the  friction  between 
the  ion  and  the  solvent.  The  nearest  approach  to  this  con- 
dition which  we  have  met  is  found  in  the  most  concentrated 
solutions  of  barium  nitrate.  Here  the  observed  molecular  low- 
ering is  about  one  per  cent  greater  than  the  calculated  value^ 


69 

An  equally  satisfactory  agreement  was  found  by  Jones  and  Stine 
for  solutions  of  potassium  chloride,  which,  likewise,  crystallizes 
without  water. 

The  values  of  M  and  H  also  show  that  the  abnormality  of 
the  freezing  point  lowering  in  the  dilute  solutions  is  greatly 
augmented  by  the  relatively  great  hydrating  power  of  the 
ions. 

Since,  then,  the  hydration  of  the  ion  increases  with  increase 
in  dilution,  the  volume  and  mass  of  the  ionic  complex  is  greater, 
the  more  dilute  the  solution;  and,  therefore,  the  greater  will 
be  the  resistance  to  be  overcome  by  the  ion  as  it  moves  through 
the  solvent.  This  being  the  case,  the  dissociation  as  meas- 
ured by  the  conductivity  method  will  be  less  than  the  true 
dissociation,  and  the  abnormality  in  the  dissociation  meas- 
ured will  increase  with  increasing  dilution. 

The  effect  produced  by  adding  more  of  the  given  electro- 
lyte will  be  to  break  down  these  larger  hydrates  into  simpler 
ones  with  smaller  volume,  thus  decreasing  the  resistance  to 
the  motion  of  the  hydrated  ion. 

This  agrees  well  with  the  results  of  Jones  and  Uhler. 1  They 
found  that  the  number  of  ether  waves  of  different  wave 
length  with  which  a  given  particle  will  vibrate  in  resonance 
decreases  with  increasing  dilution,  thereby  producing  a  nar- 
rowing of  the  absorption  bands.  On  the  other  hand,  the  ad- 
dition of  more  of  the  same  electrolyte,  or  a  strong  dehydra- 
ting agent,  decreases  the  complexity  of  the  hydrate,  thereby 
decreasing  its  period.  As  a  result,  the  particles  are  free  to 
vibrate  in  resonance  with  a  greater  number  of  wave  lengths, 
and  the  absorption  bands  widen. 

It  will  be  seen  that,  with  the  exception  of  magnesium  chlor- 
ide, the  value  of  M,  the  total  amount  of  water  held  in  com- 
bination by  one  molecule  of  the  electrolyte,  decreases  rapidly 
in  the  dilute  solutions,  passes  through  a  minimum,  and  then 
becomes  a  linear  function  of  the  concentration. 

The  hydration  per  molecule  decreases  rapidly,  to  approxi- 
mately the  same  concentration  which  corresponds  to  a  min- 
imum in  the  freezing  point  lowering,  and  then  remains 
practically  constant  as  the  concentration  increases. 

1  Am.  Chem.  J.,  37,  126  (1907);  Carnegie  Inst.  (Washington),  Memoir  No.  60. 


70 

Eliminating  the  hydration  due  to  the  ions,  the  hydration  per 
molecule  in  solution  over  a  given  range  of  temperature  is  con- 
stant, just  as  the  amount  of  water  with  which  that  same  salt 
will  crystallize  from  solution  is  constant  for  a  given  range  of 
temperature.  This  relation  is  best  illustrated  by  the  curves 
representing  the  values  of  H.  They  are  almost  asymptotic 
to  the  coordinates. 

Having  found  that  the  ions  of  a  salt  are  hyd rated,  the  next 
question  which  arises  is  this:  Is  it  the  cation  or  the  anion 
which  has  the  greater  hydrating  power? 

Nernst,  Garrard,  and  Oppermann,1  in  a  study  of  the  con- 
centration changes  which  take  place  in  an  indifferent  sub- 
stance during  electrolysis,  have  calculated  that  the  ions  SO4, 

Cl,  Br,  and  NO3  drag  with  them  9,  5,  4,  and  2.5  molecules  of 
water,  respectively. 

It  is  seen  from  a  study  of  the  chlorides  and  nitrates  of  the 
copper  group,  each  of  which  crystallizes  with  6  molecules 
of  water  (copper  chloride  alone  separating  with  two  mole- 
cules), that  the  hydration  per  molecule  is  approximately  the 
same  for  all  of  these  salts.  If,  as  Nernst  and  his  coworkers 

have  found,  the  hydrating  power  of  the  NO3  ion  is  only  one- 
half  that  of  the  Cl  ion,  then  we  should  expect  the  influence 
of  the  hydrating  power  of  these  two  anions  to  manifest  itself 
in  the  hydrating  power  of  the  salts  in  question,  and  especially 
so  since  the  three  cations  are  so  nearly  alike  chemically.  On 
the  basis  of  this  reasoning  we  are  forced  to  conclude  that  the 
hydrating  power  of  any  salt  is  primarily  a  function  of  the  cation. 

We  do  not  deny  that  the  anions  are  capable  of  forming  hy- 
drates ;  but,  if  they  do,  experiments  lead  us  to  believe  that 
they  have  this  power  only  to  a  relatively  slight  degree. 

We  have  noted  also  this  striking  relation.  It  is  well  known 
that  if  the  atomic  volumes  of  the  elements  are  plotted  as  or- 
dinates  against  the  atomic  weights  as  abscissas,  there  exists 
between  them  a  periodic  relation.  At  the  maxima  of  the  curve 
are  the  alkali  metals.  The  three  elements  having  the  largest 

1  Gottingen  Nachr.,  1900,  p.  86. 


atomic  volumes  are  potassium,  rubidium,  and  caesium.  Salts 
of  these  metals  usually  crystallize  from  aqueous  solution  in 
the  anhydrous  form,  and  as  experiments  have  shown,  they 
have  very  slight  hydrating  power  in  solution.  Lithium  and 
sodium,  some  of  Whose  salts  crystallize  with  two  and  three 
molecules  of  water,  have  much  smaller  atomic  volumes. 

At  the  minimum  of  the  third  section  of  the  atomic  weight 
curve  we  find  the  elements  strontium,  iron,  cobalt,  copper, 
and  nickel.  The  salts  of  these  metals  crystallize  with  large 
amounts  of  water  and  show  great  hydrating  power  in  solu- 
tion. Aluminium,  which  has  less  than  half  the  atomic  weight 
of  iron,  but  slightly  greater  atomic  volume,  lies  at  the  second 
minimum.  Its  salts  crystallize  with  8  and  9  molecules  of 
water  and  show  great  hydrating  power  in  solution. 

Comparing  the  metals  of  the  alkaline  earth  group  we  find 
that  barium,  whose  salts  crystallize  with  two  molecules  of 
water  or  water-free,  has  the  largest  atomic  volume.  The 
other  members  of  this  group  form  salts  which  crystallize 
with  6  molecules,  calcium  nitrate  excepted.  The  magne- 
sium cation,  which  has  the  smallest  atomic  volume,  has  the 
greatest  hydrating  power  in  solution;  the  strontium  cation, 
which  has  the  largest  atomic  volume,  has  a  smaller  hydra- 
ting  power  than  does  the  calcium  cation,  whose  atomic  vol- 
ume is  slightly  less. 

This  is  conclusive  evidence  that  the  hydrating  power  of  the 
cation  is  an  inverse  function  of  its  atomic  volume. 

That  the  velocities  of  the  ions  are  an  inverse  function  of 
their  mass  (and  perhaps  of  their  volumes)  is  an  established 
fact.  Experimental  evidence,  however,  seems  at  variance 
with  this  statement.  We  should  expect  those  ions  which 
have  the  smallest  atomic  volumes  to  have  the  greatest  migra- 
tion velocities.  On  the  contrary,  we  find  that  potassium, 
rubidium,  and  caesium  have  the  greatest  migration  veloci- 

+ 
ties  (H  and  OH  excepted),  while  the  ions  of  the  iron  and 

copper  groups,  with  very  small  atomic  volumes,  have  the 
smallest  migration  velocities. 

A  glance  at  the  two  curves  representing  the  relation  be- 
tween atomic  volume  and  atomic  weights,  and  between  migra- 


72 

tion  velocities  and  atomic  weights,  shows  at  once  the  cause 
of  this  apparent  anomaly.  It  has  been  shown  that  those 
elements  which  have  the  smallest  atomic  volumes  have  the 
greatest  hydrating  power,  and  vice  versa.  We  see,  then,  that 
those  ions  which  have  the  smallest  migration  velocities  have  also 
the  greatest  hydrating  power. 

A  somewhat  detailed  comparison  of  the  members  of  the 
different  groups  will  bring  out  this  idea  more  clearly. 

The  atomic  volumes  of  potassium,  rubidium,  and  caesium 
increase  rapidly  with  increasing  atomic  weights,  and,  as  a 
rule,  their  salts  crystallize  without  water.  We  should  ex- 
pect, then,  the  potassium  ion  to  have  the  greatest  migration 
velocity,  and  the  caesium  ion  to  have  the  smallest.  Ex- 
periments show  that  they  have  approximately  the  same  migra- 
tion velocities.  Sodium  and  lithium,  whose  atomic  volumes 
are  less  than  half  that  of  potassium,  have  migration  veloci- 
ties which  are  only  about  two-thirds  that  of  potassium. 
It  will  be  remembered  that  sodium  and  lithium  form  salts 
which  may  crystallize  with  2  and  3  molecules  of  water,  re- 
spectively. Hence  we  may  assume  that  the  increase  in  vol- 
ume of  the  sodium  and  lithium  ions,  due  to  the  formation 
of  a  relatively  large  hydrate,  decreases  the  velocity  of  those 
ions  to  a  far  greater  extent  than  the  slight  hydration  of  the 
large  potassium  ion  decreases  the  velocity  of  that  ion. 

The  atomic  volume  of  lithium  is  about  one-half  that  of 
sodium,  and  the  maximum  amount  of  water  with  which  lith- 
ium salts  crystallize  from  solution  is  3  molecules,  whereas 
the  maximum  for  sodium  salts  is  2  molecules.  Since  the 
ratio  of  2 : 3  represents  approximately  the  ratio  of  the  hydra- 
ting  power  of  the  two  ions  in  solution,  we  should  expect  the 
effect,  upon  the  velocity,  of  the  greater  increase  in  the  vol- 
ume of  the  small  lithium  ion,  due  to  its  hydration,  to  compen- 
sate somewhat  for  the  smaller  increase  in  the  volume  of  the 
larger  sodium  ion.  Experiment  shows  that  the  migration 
velocities  are  nearly  equal. 

The  same  relation  holds  for  the  metals  of  the  alkaline 
earth  group.  The  atomic  volumes  increase  with  increasing 
atomic  weight.  The  migration  velocities  of  the  cations  cal- 


73 

cium  and  strontium,  whose  salts  crystallize  with  6  molecules 
of  water,  are  approximately  equal  to  that  of  the  barium 
cation,  whose  salts  crystallize  either  with  2  molecules  of  water, 
or  water-free.  On  the  other  hand,  the  magnesium  cation, 
which  has  one-half  the  atomic  volume  of  the  calcium  ion, 
has  nearly  the  same  migration  velocity,  due  to  compensation 
between  the  atomic  volumes  and  the  hydration  of  the  ions. 

The  calcium  ion  has  a  slightly  greater  atomic  volume  than 
sodium,  yet,  owing  to  its  much  greater  hydrating  power,  its 
migration  velocity  is  considerably  less. 

The  cations  of  copper,  cobalt,  and  nickel  have  nearly  the 
same  atomic  volumes  and  the  same  hydrating  power.  We 
should  expect  them  to  have  the  same  migration  velocity, 
and  such  is  the  case. 

The  atomic  volumes  of  the  halogens,  chlorine,  bromine,  and 
iodine,  are  approximately  the  same.  If  their  ions  are  hy- 
drated  we  should  expect  them  to  combine  with  the  same  amount 
of  water,  and,  therefore,  they  should  give  migration  veloci- 
ties of  the  same  order  of  magnitude.  This  has  been  found  to 
be  the  case.  The  atomic  volume  of  fluorine  has  not  been  de- 
termined, but  from  its  position  on  the  migration  velocity 
curve  we  should  infer  that  its  atomic  volume  is  smaller  than 
that  of  the  halogens,  and  that  its  ion  possesses  a  considera- 
ble degree  of  hydrating  power. 

Further,  it  will  be  noted  that  the  migration  velocities  of 
the  halogens  are  almost  identical  with  those  of  the  alkalis 
standing  next  above  them  in  order  of  atomic  weights,  whereas 
their  atomic  volumes  are  very  much  smaller.  This  leads  us 
to  believe  that  the  compensation,  which  brings  about  an 
equalization  of  the  migration  velocities  of  the  two  groups,  is 
due  to  the  increase  in  volume  of  the  alkali  ions  by  hydration. 

The  silver  ion  alone  of  all  the  metallic  elements  for  which 
satisfactory  data  can  be  found  presents  an  exception.  It 
has  a  small  atomic  volume,  and  its  salts  crystallize  from  solu- 
tion without  water.  We  should  expect  it  to  have  but  slight 
hydrating  power  in  solution  and  it  should,  therefore,  have  a 
high  migration  velocity,  but  this  has  been  found  to  be  slightly 
less  than  that  of  the  halogens. 


74 

According  to  the  law  of  Raoult,  the  lowering  of  the  freez- 
ing point  of  a  given  weight  of  solvent  by  a  dissolved  substance 
is  directly  proportional  to  the  amount  of  the  substance  dis- 
solved, providing  that  substance  is  a  non  electrolyte.  In 
the  case  of  electrolytes  the  lowering  produced  by  gram  molec- 
ular weights  of  the  dissolved  substances  are  greater  than  those 
produced  by  gram  molecular  weights  of  non-electrolytes. 
This  abnormality  in  the  case  of  electrolytes  is  explained  by 
the  fact  that  an  ion  and  a  molecule  lower  the  freezing  point 
to  the  same  extent. 

The  fact  is  that  the  freezing  point  method  gives  us  a  rela- 
tion between  the  amount  of  solvent  acting  as  such  and  the 
number  of  dissolved  particles,  whether  they  are  molecules 
or  ions. 

Having  determined  the  freezing  point  lowering  for  any 
concentration  of  a  given  electrolyte,  it  is  an  easy  matter  to- 
calculate  the  amount  of  dissociation.  For  binary  electro- 
lytes a  is  obtained  from  the  expression  a  =  i — i,  where  i  is 

the  van't  Hoff  i.     For  ternary  electrolytes,   a  =  -    — ,   and 

i —  i 

for  quaternary  electrolytes  a  =  . 

o 

We  have  calculated  the  values  of  a  from  the  molecular 
lowerings  of  all  the  solutions  studied,  for  the  dilute  solutions 
up  to  the  concentration  at  which  the  molecular  lowering 
passes  through  a  minimum.  Beyond  this  concentration 
the  molecular  lowering  of  the  freezing  point  increases,  due  to 
hydration,  and,  consequently,  the  calculated  dissociation 
would  increase.  For  that  reason  the  values  of  a  have  not 
been  calculated. 

In  the  case  of  every  salt  studied,  without  exception,  the 
dissociation  as  calculated  from  the  freezing  point  lowering  is 
higher  than  the  dissociation  as  calculated  from  the  conductivity 
measurements. 

This  will  be  seen  by  comparing  the  values  obtained  for  a 
in  the  tables  representing  the  freezing  point  and  conductivity 
measurements  for  each  salt. 

If  there  were  no  hydration,  these  values  should  be  equaL 
Since  the  freezing  point  measurements  give  us  the  most  ac- 


75 

curate  relation  between  the  amount  of  the  actual  solvent 
and  the  number  of  dissolved  particles,  it,  therefore,  must  give 
us  the  most  accurate  measure  of  the  dissociation,  when  hy- 
dration  is  taken  into  account. 

The  conductivity  of  a  solution  is,  as  we  have  seen,  depend- 
ent upon  the  number  of  ions  present,  their  velocity,  their 
mass  and  volume,  and  the  viscosity  of  the  solution.  Since 
the  temperatures  at  which  the  dilute  solutions  freeze  are  ap- 
proximately only  one-fourth  of  a  degree  or  less  below  the 
freezing  point  of  pure  water — the  temperature  at  which  the 
conductivity  measurements  were  made — we  must  conclude 
that  the  number  of  ions  present  and  their  velocities  are  in  the 
two  cases  the  same.  Similarly,  the  viscosity  of  the  solutions 
is  the  same  in  both  measurements  and,  therefore,  the  fric- 
tion between  solvent  and  ion  will  vary  directly  as  the  sur- 
face of  the  latter. 

We  have  shown  that  most  metallic  ions  in  solution  have 
great  hydrating  power,  and  that  the  degree  of  hydration  varies, 
inversely  with  the  atomic  volume  of  the  ion.  Those  ions  which, 
have  the  greatest  hydrating  power  are  those  which  have  the 
smallest  atomic  volumes,  and  should,  therefore,  if  there  were 
no  hydration,  meet  with  less  friction  in  their  movements 
through  the  solution.  They  should  have  greater  migration 
velocities,  while  exactly  the  opposite  results  are  found. 

A  comparison  of  the  values  of  a  for  a  dilute  solution  of  the- 
strong  acids  shows  that  the  dissociation  as  measured  by  con- 
ductivity is  greater  in  every  case  than  the  dissociation  meas- 
ured by  the  freezing  point  method.  In  the  more  concentra- 
ted solutions  the  observed  freezing  point  lowerings  are  higher 
than  the  molecular  lowerings  calculated  from  conductivity.. 
This  is  due  to  the  fact  that  the  molecules  or  ions  of  those 
acids  have  considerable  hydrating  power,  and  we  obtain  in 
concentrated  solutions  results  of  the  same  character  as  with 
the  salts.  * 

Summary. 

i.  The  freezing  point  lowerings  and  the  conductivities  of 
solutions  of  a  number  of  electrolytes,  over  a  wide  range  of 
concentration,  have  been  carefully  redetermined. 


76 

2.  We  observe  that  the  molecular  lowerings  of  the  freezing 
point  of  all  the  electrolytes  studied  passes  through  a  very 
pronounced    minimum    at    concentrations    ranging   from    o.i 
to   0.25    normal.     The   molecular   lowerings   calculated   from 
the  dissociation,  as  measured  by  conductivity,  decrease  regu- 
larly from  the  most  dilute  to  the  most  concentrated  solutions. 

3.  The  magnitude  of  the  molecular  lowerings  produced  by 
molecular  quantities  of  different  salts  varies  directly  as  the 
number  of  molecules  of  water  with  which  those  salts  crystal- 
lize from  solution.     The  magnitude  of  the  hydrating  power  of 
salts   in  solution    is,  in  turn,   proportional  to  the  amount  of 
water  of  crystallization. 

4.  That  the  ions  have  very  great  hydrating  power  is  shown 
by  the  values  of  M  and  H  for  the  different  salts.     The  total 
amount  of  combined  water  decreases  with  increase  in  concen- 
tration, passes  through  a  minimum,  and  then  increases  regu- 
larly with   increase  in  concentration.     The  amount  of  water 
held  in  combination  by  one  molecule  of  a  salt  is  very  large  in 
the  more   dilute   solutions  where  the  ions  predominate.     It 
decreases  rapidly  with  decrease  in  dissociation,  and  approaches 
a  constant  value  at  greater  concentration. 

5.  The  hydrating  power  of  a  salt  is,  primarily,  a  function  of 
the  cation.      The  results  show  that  two  salts  which  crystal- 
lize with  the  same  amounts  of  water  of  crystallization  and 
contain  a  common    cation  exhibit  hydrating  power  of  the 
same  order  of  magnitude. 

6.  It  has  been  found  that  the  hydrating  power  of  a  cation 
is  an  inverse  function  of  its  atomic  volume.     Those  cations 
which  have  the  smallest  atomic  volumes  have  the  greatest 
hydrating  power,  and  vice  versa.     We  may  state  the  relations 
thus :     The  hydrating  power  of  the  ions  is  an  inverse  function  of 
their  atomic  volumes,  and  a  periodic  function  of  their  atomic 
weights. 

7.  Furthermore,  we  have  found  that  those  cations  which 
have  the  greatest  migration  velocities  exhibit,  also,  the  small- 
est hydrating  power,  and  vice  versa.     This  probably  accounts 
for  the  apparent  anomaly  which  exists  in  the  relation  between 
the  migration  velocities  of  the  ions  and  their  atomic  weights 
and    atomic    volumes.     The    influence    upon    the    migration 


77 

velocity  of  the  hydration  of  those  ions  with  small  atomic 
volumes  is  greater  than  that  of  the  small  hydration  of  those 
ions  which  have  large  atomic  volumes. 

8.  In  the  case  of  every  salt  it  has  been  found  that  the  disso- 
ciation in  the  dilute  solutions,  as  measured  by  the  conduc- 
tivity method,  is  less  than  that  calculated  from  the  freezing 
point  lowering.  Since  the  freezing  point  and  conductivity 
measurements  of  the  dilute  solutions  were  made  at  approx- 
imately the  same  temperature,  the  number  of  the  ions  pres- 
ent,- their  velocities,  and  their  hydration  are  practically  the 
same  in  both  cases.  The  solutions  have,  likewise,  the  same 
viscosity.  Therefore,  the  friction  between  the  solvent  and 
ion  will  vary  directly  as  the  surface  of  the  latter.  This  being 
the  case,  the  greater  the  dilution,  the  greater  will  be  the  com- 
plexity of  the  hydrate,  and,  consequently,  its  surface.  We 
should  expect  to  find,  therefore,  a  greater  abnormality  in  the 
dissociation,  as  measured  by  the  two  methods,  the  greater 
the  dilution  at  which  the  measurements  are  made.  The  re- 
sults show  this  to  be  the  fact. 

It  is  only  in  case  of  those  salts  which  crystallize  in  the  an- 
hydrous condition  that  we  obtain  comparable  values  for  the 
dissociation,  as  measured  by  the  two  methods.  These  values 
are  found  only  in  those  concentrations  which  lie  close  to  that, 
concentration  which  gives  the  minimum  molecular  lowering. 


BIOGRAPHY. 

James  Newton  Pearce,  the  author  of  this  dissertation,  was 
born  in  Oswego,  Illinois,  December  21,  1873.  His  early  edu- 
cation was  obtained  in  the  public  schools  of  his  native  vil- 
lage. In  1891,  at  the  age  of  17,  he  entered  the  Academy  of 
Northwestern  University,  at  Evanston,  111.,  where  he  com- 
pleted his  preparation  for  college.  In  1892  he  matriculated 
in  Northwestern  University,  graduating  in  1896  with  the  de- 
gree of  Ph.B.,  and  the  following  year  he  took  his  Master's  de- 
gree in  Chemistry  from  the  same  institution. 

From  June,  1897,  to  January,  1900,  he  was  head  chemist 
for  James  S.  Kirk  &  Co.,  soap  manufacturers  at  Chicago, 
111.  In  January,  1900,  he  entered  Chicago  University  to  pur- 
sue graduate  work  in  chemistry.  In  September  of  the  same 
year  he  was  appointed  Instructor  in  Chemistry  and  Physics 
in  the  La  Salle-Peru  Township  High  School  at  La  Salle,  111., 
where  he  remained  for  two  years.  In  1902  he  was  appointed 
Instructor  in  Chemistry  in  Northwestern  University  and  re- 
mained there  until  1905,  when  he  entered  Johns  Hopkins 
University  as  a  graduate  student  in  Chemistry.  His  subor- 
dinate subjects  were  Physical  Chemistry  and  Physics. 


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